8'1

Briefly answer the following questions. (a) What is a null hypothesisH₀?Any hypothesis that differs from the original claim being made.A specific hypothesis where the claim is that the population parameter is equal to 0. A specific hypothesis where the claim is that the population parameter does not equal 0.A working hypothesis making a claim about the population parameter in question.

(b) What is an alternate hypothesisH₁?Any hypothesis that differs from the original claim being made.A specific hypothesis where the claim is that the population parameter does not equal 0. A working hypothesis making a claim about the population parameter in question.A specific hypothesis where the claim is that the population parameter is equal to 0.

(c) What is a type I error? Type I error is rejecting the null hypothesis when it is false.Type I error is failing to reject the null hypothesis when it is false. Type I error is rejecting the null hypothesis when it is true.Type I error is failing to reject the null hypothesis when it is true.

What is a type II error?Type II error is rejecting the null hypothesis when it is false.Type II error is failing to reject the null hypothesis when it is false. Type II error is rejecting the null hypothesis when it is true.Type II error is failing to reject the null hypothesis when it is true.

(d) What is the level of significance of a test? The probability of a type II error.The probability of a type I error.

What is the probability of a type II error? 11

2.

[-/0.22 Points]DETAILSBBUNDERSTAT12 8.1.011.MI.SA.

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This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any points for the skipped part, and you will not be able to come back to the skipped part.

Tutorial Exercise

Suppose you want to test the claim that a population mean equals31.(a) State the null hypothesis. (b) State the alternate hypothesis if you have no information regarding how the population mean might differ from31. (c) State the alternative hypothesis if you believe (based on experience or past studies) that the population mean may exceed31. (d) State the alternative hypothesis if you believe (based on experience or past studies) that the population mean may be less than31.

Step 1

(a) State the null hypothesis.

Our first step is to establish a working hypothesis about the population parameter in question. This hypothesis is called the null hypothesis,

H₀.

Here the population parameter in question is the mean. The statement that is under investigation is that this mean is equal to .Therefore, we have the following null hypothesis.

H₀: ? > < = 31

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[-/0.22 Points]DETAILSBBUNDERSTAT12 8.1.011.MI.

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Suppose you want to test the claim that a population mean equals40.(a) State the null hypothesis. H₀:>40H₀:<40 H₀:= 40H₀:40H₀:40

(b) State the alternate hypothesis if you have no information regarding how the population mean might differ from40. H₁:>40H₁:<40 H₁:= 40H₁:40H₁:40

(c) State the alternative hypothesis if you believe (based on experience or past studies) that the population mean may exceed40. H₁:>40H₁:<40 H₁:= 40H₁:40H₁:40

(d) State the alternative hypothesis if you believe (based on experience or past studies) that the population mean may be less than40. H₁:>40H₁:<40 H₁:= 40H₁:40H₁:40

4.

[-/0.22 Points]DETAILSBBUNDERSTAT12 8.1.015.MI.

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The body weight of a healthy 3-month-old colt should be about=62kg.(a) If you want to set up a statistical test to challenge the claim that=62kg, what would you use for the null hypothesis

H₀?

> 62 kg< 62 kg = 62 kg62 kg

(b) In Nevada, there are many herds of wild horses. Suppose you want to test the claim that the average weight of a wild Nevada colt (3 months old) is less than62kg.What would you use for the alternate hypothesis

H₁?

> 62 kg< 62 kg = 62 kg62 kg

(c) Suppose you want to test the claim that the average weight of such a wild colt is greater than62kg. What would you use for the alternate hypothesis? > 62 kg< 62 kg = 62 kg62 kg

(d) Suppose you want to test the claim that the average weight of such a wild colt isdifferentfrom62kg. What would you use for the alternate hypothesis? > 62 kg< 62 kg = 62 kg62 kg

(e) For each of the tests in parts (b), (c), and (d), respectively, would the area corresponding to theP-value be on the left, on the right, or on both sides of the mean? both; left; rightleft; right; both right; left; bothleft; both; right

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[-/0.22 Points]DETAILSBBUNDERSTAT12 8.1.015.MI.SA.

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This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any points for the skipped part, and you will not be able to come back to the skipped part.

Tutorial Exercise

The body weight of a healthy 3-month-old colt should be about = 73 kg.(a) If you want to set up a statistical test to challenge the claim that = 73 kg, what would you use for the null hypothesis

H₀?

(b) In Nevada, there are many herds of wild horses. Suppose you want to test the claim that the average weight of a wild Nevada colt (3 months old) is less than 73 kg. What would you use for the alternate hypothesis

H₁?

(c) Suppose you want to test the claim that the average weight of such a wild colt is greater than 73 kg. What would you use for the alternate hypothesis? (d) Suppose you want to test the claim that the average weight of such a wild colt is different from 73 kg. What would you use for the alternate hypothesis? (e) For each of the tests in parts (b), (c), and (d), respectively, would the area corresponding to the P-value be on the left, on the right, or on both sides of the mean?

Step 1

(a) If you want to set up a statistical test to challenge the claim that = 73 kg, what would you use for the null hypothesis

H₀?

Recall that in hypothesis testing, the null hypothesis

H₀

is the statement or claim about a parameter, and the alternate hypothesis

H₁

is the statement that will be adopted if there is evidence that

H₀

should be rejected. We want to challenge the claim that = 73 kg. That is, we want to test whether the body weight of a 3-month-old colt is ---Select--- equal to not equal to less than greater than 73 kg, or if there is evidence to reject this claim in favor of an alternate statement. Therefore, the null hypothesis is

H₀: ? = < > 73 kg.

6.

[-/0.22 Points]DETAILSBBUNDERSTAT12 8.1.016.

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How much customers buy is a direct result of how much time they spend in the store. A study of average shopping times in a large national houseware store gave the following information (Source:Why We Buy: The Science of Shoppingby P. Underhill).Women with female companion: 8.3 min. Women with male companion: 4.5 min.

Suppose you want to set up a statistical test to challenge the claim that a woman with a female friend spends an average of 8.3 minutes shopping in such a store.(a) What would you use for the null and alternate hypotheses if you believe the average shopping time is less than 8.3 minutes?H_o:= 8.3;H₁:> 8.3H_o:< 8.3;H₁:= 8.3 H_o:= 8.3;H₁:< 8.3H_o:= 8.3;H₁:8.3

Is this a right-tailed, left-tailed, or two-tailed test?two-tailedright-tailed left-tailed

(b) What would you use for the null and alternate hypotheses if you believe the average shopping time is different from 8.3 minutes?H_o:= 8.3;H₁:< 8.3H_o:= 8.3;H₁:8.3 H_o:= 8.3;H₁:> 8.3H_o:8.3;H₁:= 8.3

Is this a right-tailed, left-tailed, or two-tailed test?left-tailedright-tailed two-tailed

Stores that sell mainly to women should figure out a way to engage the interest of men! Perhaps comfortable seats and a big TV with sports programs. Suppose such an entertainment center was installed and you now wish to challenge the claim that a woman with a male friend spends only 4.5 minutes shopping in a houseware store.(c) What would you use for the null and alternate hypotheses if you believe the average shopping time is more than 4.5 minutes?H_o:= 4.5;H₁:4.5H_o:= 4.5;H₁:< 4.5 H_o:> 4.5;H₁:= 4.5H_o:= 4.5;H₁:> 4.5

Is this a right-tailed, left-tailed, or two-tailed test?right-tailedtwo-tailed left-tailed

(d) What would you use for the null and alternate hypotheses if you believe the average shopping time is different from 4.5 minutes?H_o:= 4.5;H₁:< 4.5H_o:4.5;H₁:= 4.5 H_o:= 4.5;H₁:4.5H_o:= 4.5;H₁:> 4.5

Is this a right-tailed, left-tailed, or two-tailed test?right-tailedleft-tailed two-tailed

7.

[-/0.22 Points]DETAILSBBUNDERSTAT12 8.1.017.

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Weatherwisemagazine is published in association with the American Meteorological Society. Volume 46, Number 6 has a rating system to classify Nor'easter storms that frequently hit New England states and can cause much damage near the ocean coast. Aseverestorm has an average peak wave height of 16.4 feet for waves hitting the shore. Suppose that a Nor'easter is in progress at the severe storm class rating.(a) Let us say that we want to set up a statistical test to see if the wave action (i.e., height) is dying down or getting worse. What would be the null hypothesis regarding average wave height?> 16.4= 16.4 < 16.416.4

(b) If you wanted to test the hypothesis that the storm is getting worse, what would you use for the alternate hypothesis?= 16.416.4 > 16.4< 16.4

(c) If you wanted to test the hypothesis that the waves are dying down, what would you use for the alternate hypothesis?= 16.4> 16.4 16.4< 16.4

(d) Suppose you do not know if the storm is getting worse or dying out. You just want to test the hypothesis that the average wave height isdifferent(either higher or lower) from the severe storm class rating. What would you use for the alternate hypothesis?16.4= 16.4 > 16.4< 16.4

(e) For each of the tests in parts (b), (c), and (d), would the area corresponding to theP-value be on the left, on the right, or on both sides of the mean?left; right; bothright; left; both both; left; rightleft; both; right

8.

[-/0.22 Points]DETAILSBBUNDERSTAT12 8.1.018.

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Consumer Reportsstated that the mean time for a Chrysler Concorde to go from 0 to 60 miles per hour was 8.7 seconds.(a) If you want to set up a statistical test to challenge the claim of 8.7 seconds, what would you use for the null hypothesis?8.7= 8.7 < 8.7> 8.7

(b) The town of Leadville, Colorado, has an elevation over 10,000 feet. Suppose you wanted to test the claim that the average time to accelerate from 0 to 60 miles per hour is longer in Leadville (because of less oxygen). What would you use for the alternate hypothesis?= 8.7> 8.7 8.7< 8.7

(c) Suppose you made an engine modification and you think the average time to accelerate from 0 to 60 miles per hour is reduced. What would you use for the alternate hypothesis?= 8.7> 8.7 < 8.78.7

(d) For each of the tests in parts (b) and (c), would theP-value area be on the left, on the right, or on both sides of the mean?left; bothleft; right right; leftboth; left

9.

[-/0.22 Points]DETAILSBBUNDERSTAT12 8.1.019.

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Letxbe a random variable representing dividend yield of bank stocks. We may assume thatxhas a normal distribution with=3.3%.A random sample of10 bankstocks gave the following yields (in percents).

5.7

4.8

6.0

4.9

4.0

3.4

6.5

7.1

5.3

6.1

The sample mean isx= 5.38%. Suppose that for the entire stock market, the mean dividend yield is=4.0%.Do these data indicate that the dividend yield of all bank stocks is higher than4.0%? Use=0.01. (a) What is the level of significance? State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test? H₀:= 4%;H₁:> 4%; right-tailedH₀:= 4%;H₁:4%; two-tailed H₀:> 4%;H₁:= 4%; right-tailedH₀:= 4%;H₁:< 4%; left-tailed

(b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. The standard normal, since we assume thatxhas a normal distribution with unknown.The Student'st, sincenis large with unknown. The Student'st, since we assume thatxhas a normal distribution with known.The standard normal, since we assume thatxhas a normal distribution with known.

Compute thezvalue of the sample test statistic. (Round your answer to two decimal places.) (c) Find (or estimate) theP-value. (Round your answer to four decimal places.) Sketch the sampling distribution and show the area corresponding to theP-value.

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level? At the= 0.01 level, we reject the null hypothesis and conclude the data are statistically significant.At the= 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant. At the= 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant.At the= 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.

(e) State your conclusion in the context of the application.There is sufficient evidence at the 0.01 level to conclude that the average yield for bank stocks is higher than that of the entire stock market.There is insufficient evidence at the 0.01 level to conclude that the average yield for bank stocks is higher than that of the entire stock market.

10.

[-/0.22 Points]DETAILSBBUNDERSTAT12 8.1.020.MI.

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Gentle Ben is a Morgan horse at a Colorado dude ranch. Over the past 8 weeks, a veterinarian took the following glucose readings from this horse (in mg/100 ml).

91

88

80

103

97

112

82

87

The sample mean isx92.5. Letxbe a random variable representing glucose readings taken from Gentle Ben. We may assume thatxhas a normal distribution, and we know from past experience that= 12.5.The mean glucose level for horses should be= 85 mg/100 ml.Do these data indicate that Gentle Ben has an overall average glucose level higher than 85? Use= 0.05.

(a)

What is the level of significance?

State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test?

H₀:= 85;H₁:< 85; left-tailedH₀:= 85;H₁:> 85; right-tailed H₀:= 85;H₁:85; two-tailedH₀:> 85;H₁:= 85; right-tailed

(b)

What sampling distribution will you use? Explain the rationale for your choice of sampling distribution.

The standard normal, since we assume thatxhas a normal distribution with known.The Student'st, since we assume thatxhas a normal distribution with known. The standard normal, since we assume thatxhas a normal distribution with unknown.The Student'st, sincenis large with unknown.

Compute thezvalue of the sample test statistic. (Round your answer to two decimal places.)

(c)

Find (or estimate) theP-value. (Round your answer to four decimal places.)

Sketch the sampling distribution and show the area corresponding to theP-value.

A plot of the normal probability curve has a horizontal axis with values from3 to 3. The curve enters the window from the left, just above the horizontal axis, goes up and to the right, changes direction over approximately 0 on the horizontal axis, and then goes down and to the right before exiting the window just above the horizontal axis. The area under the curve between3 and 1.7 is shaded.

A plot of the normal probability curve has a horizontal axis with values from3 to 3. The curve enters the window from the left, just above the horizontal axis, goes up and to the right, changes direction over approximately 0 on the horizontal axis, and then goes down and to the right before exiting the window just above the horizontal axis. The area under the curve between 1.7 and 3 is shaded.

A plot of the normal probability curve has a horizontal axis with values from3 to 3. The curve enters the window from the left, just above the horizontal axis, goes up and to the right, changes direction over approximately 0 on the horizontal axis, and then goes down and to the right before exiting the window just above the horizontal axis. The area under the curve between3 and1.7 is shaded.

A plot of the normal probability curve has a horizontal axis with values from3 to 3. The curve enters the window from the left, just above the horizontal axis, goes up and to the right, changes direction over approximately 0 on the horizontal axis, and then goes down and to the right before exiting the window just above the horizontal axis. The area under the curve between3 and1.7 as well as the area under the curve between 1.7 and 3 are both shaded.

(d)

Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level?

At the= 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.At the= 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant. At the= 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.At the= 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.

(e)

State your conclusion in the context of the application.

There is sufficient evidence at the 0.05 level to conclude that the horse's glucose is higher than 85 mg/100 ml.There is insufficient evidence at the 0.05 level to conclude that the horse's glucose is higher than 85 mg/100 ml.

11.

[-/0.22 Points]DETAILSBBUNDERSTAT12 8.1.021.

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Bill Alther is a zoologist who studies Anna's hummingbird (Calypte anna).Suppose that in a remote part of the Grand Canyon, a random sample of six of these birds was caught, weighed, and released. The weights (in grams) were as follows.

3.7

2.9

3.8

4.2

4.8

3.1

The sample mean isx= 3.75 grams. Letxbe a random variable representing weights of hummingbirds in this part of the Grand Canyon. We assume thatxhas a normal distribution and=0.68gram.Suppose it is known that for the population of all Anna's hummingbirds, the mean weight is=4.50grams.Do the data indicate that the mean weight of these birds in this part of the Grand Canyon is less than4.50grams?Use=0.01.(a) What is the level of significance? State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test? H₀:< 4.5 g;H₁:= 4.5 g; left-tailedH₀:= 4.5 g;H₁:4.5 g; two-tailed H₀:= 4.5 g;H₁:> 4.5 g; right-tailedH₀:= 4.5 g;H₁:< 4.5 g; left-tailed

(b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. The Student'st, since we assume thatxhas a normal distribution with known.The standard normal, since we assume thatxhas a normal distribution with unknown. The standard normal, since we assume thatxhas a normal distribution with known.The Student'st, sincenis large with unknown.

Compute thezvalue of the sample test statistic. (Round your answer to two decimal places.) (c) Find (or estimate) theP-value. (Round your answer to four decimal places.) Sketch the sampling distribution and show the area corresponding to theP-value.

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level? At the= 0.01 level, we reject the null hypothesis and conclude the data are statistically significant.At the= 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant. At the= 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant.At the= 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.

(e) State your conclusion in the context of the application. There is sufficient evidence at the 0.01 level to conclude that humming birds in the Grand Canyon weigh less than 4.50 grams.There is insufficient evidence at the 0.01 level to conclude that humming birds in the Grand Canyon weigh less than 4.50 grams.

12.

[-/0.28 Points]DETAILSBBUNDERSTAT12 8.1.022.

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The price to earnings ratio (P/E) is an important tool in financial work. A random sample of 14 large U.S. banks (J. P. Morgan, Bank of America, and others) gave the following P/E ratios.

24

16

22

14

12

13

17

22

15

19

23

13

11

18

The sample mean is

x17.1.

Generally speaking, a low P/E ratio indicates a "value" or bargain stock. Suppose a recent copy of a magazine indicated that theP/E ratioof a certain stock index is=18.Letxbe a random variable representing theP/E ratioof all largeU.S. bankstocks. We assume thatxhas a normal distribution and=3.5.Do these data indicate that theP/E ratioof allU.S. bankstocks is less than18? Use=0.01.(a) What is the level of significance? State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test? H₀:= 18;H₁:< 18; left-tailedH₀:= 18;H₁:18; two-tailed H₀:18;H₁:= 18; two-tailedH₀:= 18;H₁:> 18; right-tailed

(b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. The standard normal, since we assume thatxhas a normal distribution with unknown.The Student'st, sincenis large with unknown. The standard normal, since we assume thatxhas a normal distribution with known.The Student'st, since we assume thatxhas a normal distribution with known.

Compute thezvalue of the sample test statistic. (Round your answer to two decimal places.) (c) Find (or estimate) theP-value. (Round your answer to four decimal places.) Sketch the sampling distribution and show the area corresponding to theP-value.

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level? At the= 0.01 level, we reject the null hypothesis and conclude the data are statistically significant.At the= 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant. At the= 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant.At the= 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.

(e) State your conclusion in the context of the application. There is sufficient evidence at the 0.01 level to conclude that the P/E ratio of all large U.S. bank stocks is less than 18There is insufficient evidence at the 0.01 level to conclude that the P/E ratio of all large U.S. bank stocks is less than 18

8'2

1.

[-/0.27 Points]DETAILSBBUNDERSTAT12 8.2.011.

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Weatherwiseis a magazine published by the American Meteorological Society. One issue gives a rating system used to classify Nor'easter storms that frequently hit New England and can cause much damage near the ocean. A severe storm has an average peak wave height of= 16.4 feet for waves hitting the shore. Suppose that a Nor'easter is in progress at the severe storm class rating. Peak wave heights are usually measured from land (using binoculars) off fixed cement piers. Suppose that a reading of40waves showed an average wave height ofx=16.9feet. Previous studies of severe storms indicate that= 3.5feet. Does this information suggest that the storm is (perhaps temporarily) increasing above the severe rating? Use= 0.01.(a) What is the level of significance? State the null and alternate hypotheses.H₀:= 16.4 ft;H₁:16.4 ftH₀:> 16.4 ft;H₁:= 16.4 ft H₀:= 16.4 ft;H₁:< 16.4 ftH₀:= 16.4 ft;H₁:> 16.4 ftH₀:< 16.4 ft;H₁:= 16.4 ft

(b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution.The standard normal, since the sample size is large andis known.The Student'st, since the sample size is large andis unknown. The Student'st, since the sample size is large andis known.The standard normal, since the sample size is large andis unknown.

What is the value of the sample test statistic? (Round your answer to two decimal places.) (c) Estimate theP-value. P-value > 0.2500.100 <P-value < 0.250 0.050 <P-value < 0.1000.010 <P-value < 0.050P-value < 0.010

Sketch the sampling distribution and show the area corresponding to theP-value.

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level?At the= 0.01 level, we reject the null hypothesis and conclude the data are statistically significant.At the= 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant. At the= 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant.At the= 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.

(e) Interpret your conclusion in the context of the application.There is sufficient evidence at the 0.01 level to conclude that the storm is increasing above the severe rating.There is insufficient evidence at the 0.01 level to conclude that the storm is increasing above the severe rating.

2.

[-/0.27 Points]DETAILSBBUNDERSTAT12 8.2.012.MI.S.

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Letxbe a random variable that represents the pH of arterial plasma (i.e., acidity of the blood). For healthy adults, the mean of thexdistribution is= 7.4.A new drug for arthritis has been developed. However, it is thought that this drug may change blood pH. A random sample of31patients with arthritis took the drug for 3 months. Blood tests showed thatx=8.4with sample standard deviations=2.5.Use a 5% level of significance to test the claim that the drug has changed (either way) the mean pH level of the blood.

(a)

What is the level of significance?

State the null and alternate hypotheses.

H₀:> 7.4;H₁:= 7.4H₀:= 7.4;H₁:7.4 H₀:= 7.4;H₁:< 7.4H₀:7.4;H₁:= 7.4H₀:= 7.4;H₁:> 7.4

(b)

What sampling distribution will you use? Explain the rationale for your choice of sampling distribution.

The standard normal, since the sample size is large andis known.The standard normal, since the sample size is large andis unknown. The Student'st, since the sample size is large andis known.The Student'st, since the sample size is large andis unknown.

What is the value of the sample test statistic? (Round your answer to three decimal places.)

(c)

Estimate theP-value.

P-value > 0.1500.100 <P-value < 0.150 0.050 <P-value < 0.1000.020 <P-value < 0.050P-value < 0.020

Sketch the sampling distribution and show the area corresponding to theP-value.

A plot of the Student's t-probability curve has a horizontal axis with values from4 to 4. The curve enters the window from the left, just above the horizontal axis, goes up and to the right, changes direction over approximately 0 on the horizontal axis, and then goes down and to the right before exiting the window just above the horizontal axis. The area under the curve between4 and2.23 is shaded.

A plot of the Student's t-probability curve has a horizontal axis with values from4 to 4. The curve enters the window from the left, just above the horizontal axis, goes up and to the right, changes direction over approximately 0 on the horizontal axis, and then goes down and to the right before exiting the window just above the horizontal axis. The area under the curve between2.23 and 4 is shaded.

A plot of the Student's t-probability curve has a horizontal axis with values from4 to 4. The curve enters the window from the left, just above the horizontal axis, goes up and to the right, changes direction over approximately 0 on the horizontal axis, and then goes down and to the right before exiting the window just above the horizontal axis. The area under the curve between4 and2.23 as well as the area under the curve between 2.23 and 4 are both shaded.

A plot of the Student's t-probability curve has a horizontal axis with values from4 to 4. The curve enters the window from the left, just above the horizontal axis, goes up and to the right, changes direction over approximately 0 on the horizontal axis, and then goes down and to the right before exiting the window just above the horizontal axis. The area under the curve between 2.23 and 4 is shaded.

(d)

Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level?

At the= 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.At the= 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant. At the= 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.At the= 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.

(e)

Interpret your conclusion in the context of the application.

There is sufficient evidence at the 0.05 level to conclude that the drug has changed the mean pH level of the blood.There is insufficient evidence at the 0.05 level to conclude that the drug has changed the mean pH level of the blood.

3.

[-/0.27 Points]DETAILSBBUNDERSTAT12 8.2.013.S.

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A random sample of51adult coyotes in a region of northern Minnesota showed the average age to bex=2.03years, with sample standard deviations=0.82years. However, it is thought that the overall population mean age of coyotes is= 1.75.Do the sample data indicate that coyotes in this region of northern Minnesota tend to live longer than the average of 1.75 years? Use= 0.01.

(a) What is the level of significance? State the null and alternate hypotheses.H₀:< 1.75 yr;H₁:= 1.75 yrH₀:= 1.75 yr;H₁:> 1.75 yr H₀:= 1.75 yr;H₁:1.75 yrH₀:> 1.75 yr;H₁:= 1.75 yrH₀:= 1.75 yr;H₁:< 1.75 yr

(b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution.The Student'st, since the sample size is large andis unknown.The Student'st, since the sample size is large andis known. The standard normal, since the sample size is large andis known.The standard normal, since the sample size is large andis unknown.

What is the value of the sample test statistic? (Round your answer to three decimal places.) (c) Estimate theP-value. P-value > 0.2500.100 <P-value < 0.250 0.050 <P-value < 0.1000.010 <P-value < 0.050P-value < 0.010

Sketch the sampling distribution and show the area corresponding to theP-value.

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level?At the= 0.01 level, we reject the null hypothesis and conclude the data are statistically significant.At the= 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant. At the= 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant.At the= 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.

(e) Interpret your conclusion in the context of the application.There is sufficient evidence at the 0.01 level to conclude that coyotes in the specified region tend to live longer than 1.75 years.There is insufficient evidence at the 0.01 level to conclude that coyotes in the specified region tend to live longer than 1.75 years.

4.

[-/0.27 Points]DETAILSBBUNDERSTAT12 8.2.014.MI.S.

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Pyramid Lake is on the Paiute Indian Reservation in Nevada. The lake is famous for cutthroat trout. Suppose a friend tells you that the average length of trout caught in Pyramid Lake is= 19inches. However, a survey reported that of a random sample of51fish caught, the mean length wasx=18.6inches, with estimated standard deviations=2.5inches. Do these data indicate that the average length of a trout caught in Pyramid Lake is less than= 19inches? Use= 0.05.

(a)

What is the level of significance?

State the null and alternate hypotheses.

H₀:< 19 in;H₁:= 19 inH₀:= 19 in;H₁:19 in H₀:= 19 in;H₁:< 19 inH₀:> 19 in;H₁:= 19 inH₀:= 19 in;H₁:> 19 in

(b)

What sampling distribution will you use? Explain the rationale for your choice of sampling distribution.

The standard normal, since the sample size is large andis known.The standard normal, since the sample size is large andis unknown. The Student'st, since the sample size is large andis unknown.The Student'st, since the sample size is large andis known.

What is the value of the sample test statistic? (Round your answer to three decimal places.)

(c)

Estimate theP-value.

P-value > 0.0100.0010 <P-value < 0.010 0.250 <P-value < 0.00100.125 <P-value < 0.250P-value < 0.125

Sketch the sampling distribution and show the area corresponding to theP-value.

A plot of the Student's t-probability curve has a horizontal axis with values from4 to 4. The curve enters the window from the left, just above the horizontal axis, goes up and to the right, changes direction over approximately 0 on the horizontal axis, and then goes down and to the right before exiting the window just above the horizontal axis. The area under the curve between 1.14 and 4 is shaded.

A plot of the Student's t-probability curve has a horizontal axis with values from4 to 4. The curve enters the window from the left, just above the horizontal axis, goes up and to the right, changes direction over approximately 0 on the horizontal axis, and then goes down and to the right before exiting the window just above the horizontal axis. The area under the curve between1.14 and 4 is shaded.

A plot of the Student's t-probability curve has a horizontal axis with values from4 to 4. The curve enters the window from the left, just above the horizontal axis, goes up and to the right, changes direction over approximately 0 on the horizontal axis, and then goes down and to the right before exiting the window just above the horizontal axis. The area under the curve between4 and1.14 as well as the area under the curve between 1.14 and 4 are both shaded.

A plot of the Student's t-probability curve has a horizontal axis with values from4 to 4. The curve enters the window from the left, just above the horizontal axis, goes up and to the right, changes direction over approximately 0 on the horizontal axis, and then goes down and to the right before exiting the window just above the horizontal axis. The area under the curve between4 and1.14 is shaded.

(d)

Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level?

At the= 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.At the= 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant. At the= 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.At the= 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.

(e)

Interpret your conclusion in the context of the application.

There is sufficient evidence at the 0.05 level to conclude that the average fish length is less than 19 inches.There is insufficient evidence at the 0.05 level to conclude that the average fish length is less than 19 inches.

5.

[-/0.27 Points]DETAILSBBUNDERSTAT12 8.2.015.S.

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Socially conscious investors screen out stocks of alcohol and tobacco makers, firms with poor environmental records, and companies with poor labor practices. Some examples of "good," socially conscious companies are Johnson and Johnson, Dell Computers, Bank of America, and Home Depot. The question is, are such stocks overpriced? One measure of value is the P/E, or price-to-earnings ratio. High P/E ratios may indicate a stock is overpriced. For the S&P Stock Index of all major stocks, the mean P/E ratio is= 19.4. A random sample of 36 "socially conscious" stocks gave a P/E ratio sample mean ofx=17.8,with sample standard deviations=5.2.Does this indicate that the mean P/E ratio of all socially conscious stocks is different (either way) from the mean P/E ratio of the S&P Stock Index? Use= 0.05.

(a) What is the level of significance? State the null and alternate hypotheses.H₀:= 19.4;H₁:< 19.4H₀:= 19.4;H₁:19.4 H₀:> 19.4;H₁:= 19.4H₀:19.4;H₁:= 19.4H₀:= 19.4;H₁:> 19.4

(b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution.The Student'st, since the sample size is large andis unknown.The standard normal, since the sample size is large andis unknown. The Student'st, since the sample size is large andis known.The standard normal, since the sample size is large andis known.

What is the value of the sample test statistic? (Round your answer to three decimal places.) (c) Estimate theP-value. P-value > 0.2500.100 <P-value < 0.250 0.050 <P-value < 0.1000.010 <P-value < 0.050P-value < 0.010

Sketch the sampling distribution and show the area corresponding to theP-value.

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level?At the= 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.At the= 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant. At the= 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.At the= 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.

(e) Interpret your conclusion in the context of the application.There is sufficient evidence at the 0.05 level to conclude that the mean P/E ratio of all socially conscious stocks differs from the mean P/E ratio of the S&P Stock Index.There is insufficient evidence at the 0.05 level to conclude that the mean P/E ratio of all socially conscious stocks differs from the mean P/E ratio of the S&P Stock Index.

6.

[-/0.27 Points]DETAILSBBUNDERSTAT12 8.2.016.MI.S.

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Unfortunately, arsenic occurs naturally in some ground water.A mean arsenic level of= 8.0parts per billion (ppb) is considered safe for agricultural use. A well in Texas is used to water cotton crops. This well is tested on a regular basis for arsenic. A random sample of41tests gave a sample mean ofx=7.1ppb arsenic, withs=2.2ppb. Does this information indicate that the mean level of arsenic in this well is less than8 ppb?Use= 0.01.

(a)

What is the level of significance?

State the null and alternate hypotheses.

H₀:> 8 ppb;H₁:= 8 ppbH₀:< 8 ppb;H₁:= 8 ppb H₀:= 8 ppb;H₁:> 8 ppbH₀:= 8 ppb;H₁:8 ppbH₀:= 8 ppb;H₁:< 8 ppb

(b)

What sampling distribution will you use? Explain the rationale for your choice of sampling distribution.

The Student'st, since the sample size is large andis unknown.The standard normal, since the sample size is large andis known. The standard normal, since the sample size is large andis unknown.The Student'st, since the sample size is large andis known.

What is the value of the sample test statistic? (Round your answer to three decimal places.)

(c)

Estimate theP-value.

P-value > 0.1000.050 <P-value < 0.100 0.010 <P-value < 0.0500.005 <P-value < 0.010P-value < 0.005

Sketch the sampling distribution and show the area corresponding to theP-value.

A plot of the Student's t-probability curve has a horizontal axis with values from4 to 4. The curve enters the window from the left, just above the horizontal axis, goes up and to the right, changes direction over approximately 0 on the horizontal axis, and then goes down and to the right before exiting the window just above the horizontal axis. The area under the curve between4 and2.62 is shaded.

A plot of the Student's t-probability curve has a horizontal axis with values from4 to 4. The curve enters the window from the left, just above the horizontal axis, goes up and to the right, changes direction over approximately 0 on the horizontal axis, and then goes down and to the right before exiting the window just above the horizontal axis. The area under the curve between4 and2.62 as well as the area under the curve between 2.62 and 4 are both shaded.

A plot of the Student's t-probability curve has a horizontal axis with values from4 to 4. The curve enters the window from the left, just above the horizontal axis, goes up and to the right, changes direction over approximately 0 on the horizontal axis, and then goes down and to the right before exiting the window just above the horizontal axis. The area under the curve between2.62 and 4 is shaded.

A plot of the Student's t-probability curve has a horizontal axis with values from4 to 4. The curve enters the window from the left, just above the horizontal axis, goes up and to the right, changes direction over approximately 0 on the horizontal axis, and then goes down and to the right before exiting the window just above the horizontal axis. The area under the curve between 2.62 and 4 is shaded.

(d)

Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level?

At the= 0.01 level, we reject the null hypothesis and conclude the data are statistically significant.At the= 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant. At the= 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant.At the= 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.

(e)

Interpret your conclusion in the context of the application.

There is sufficient evidence at the 0.01 level to conclude that the mean level of arsenic in the well is less than8 ppb.There is insufficient evidence at the 0.01 level to conclude that the mean level of arsenic in the well is less than8 ppb.

7.

[-/0.27 Points]DETAILSBBUNDERSTAT12 8.2.017.S.

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Letxbe a random variable that represents red blood cell count (RBC) in millions of cells per cubic millimeter of whole blood. Thenxhas a distribution that is approximately normal. For the population of healthy female adults, suppose the mean of thexdistribution is about4.78. Suppose that a female patient has taken six laboratory blood tests over the past several months and that the RBC count data sent to the patient's doctor are as follows.

4.9

4.2

4.5

4.1

4.4

4.3

(i) Use a calculator with sample mean and standard deviation keys to findxands. (Round your answers to two decimal places.)

x	=
s	=

(ii) Do the given data indicate that the population mean RBC count for this patient is lower than4.78? Use= 0.05.(a) What is the level of significance? State the null and alternate hypotheses.H₀:= 4.78;H₁:> 4.78H₀:= 4.78;H₁:< 4.78 H₀:< 4.78;H₁:= 4.78H₀:> 4.78;H₁:= 4.78H₀:= 4.78;H₁:4.78

(b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution.The standard normal, since we assume thatxhas a normal distribution andis known.The standard normal, since we assume thatxhas a normal distribution andis unknown. The Student'st, since we assume thatxhas a normal distribution andis unknown.The Student'st, since we assume thatxhas a normal distribution andis known.

What is the value of the sample test statistic? (Round your answer to three decimal places.) (c) Estimate theP-value. P-value > 0.2500.100 <P-value < 0.250 0.050 <P-value < 0.1000.010 <P-value < 0.050P-value < 0.010

Sketch the sampling distribution and show the area corresponding to theP-value.

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level?At the= 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.At the= 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant. At the= 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.At the= 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.

(e) Interpret your conclusion in the context of the application.There is sufficient evidence at the 0.05 level to conclude that the population mean RBC count for the patient is lower than 4.78.There is insufficient evidence at the 0.05 level to conclude that the population mean RBC count for the patient is lower than 4.78.

8.

[-/0.27 Points]DETAILSBBUNDERSTAT12 8.2.018.MI.S.

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Letxbe a random variable that represents hemoglobin count (HC) in grams per 100 milliliters of whole blood. Thenxhas a distribution that is approximately normal, with population mean of about 14 for healthy adult women. Suppose that a female patient has taken 10 laboratory blood tests during the past year. The HC data sent to the patient's doctor are as follows.

14

19

16

19

15

13

14

18

17

10

(a)

Use a calculator with sample mean and standard deviation keys to findxands. (Round your answers to two decimal places.)

x=s=

(b)

Does this information indicate that the population average HC for this patient is higher than 14? Use= 0.01.

(i)

What is the level of significance?

State the null and alternate hypotheses.

H₀:= 14;H₁:14H₀:> 14;H₁:= 14 H₀:= 14;H₁:> 14H₀:< 14;H₁:= 14H₀:= 14;H₁:< 14

(ii)

What sampling distribution will you use? Explain the rationale for your choice of sampling distribution.

The standard normal, since we assume thatxhas a normal distribution andis unknown.The standard normal, since we assume thatxhas a normal distribution andis known. The Student'st, since we assume thatxhas a normal distribution andis known.The Student'st, since we assume thatxhas a normal distribution andis unknown.

What is the value of the sample test statistic? (Round your answer to three decimal places.)

(iii)

Estimate theP-value.

P-value > 0.2500.200 <P-value < 0.250 0.075 <P-value < 0.2000.050 <P-value < 0.075P-value < 0.050

Sketch the sampling distribution and show the area corresponding to theP-value.

A plot of the Student's t-probability curve has a horizontal axis with values from4 to 4. The curve enters the window from the left, just above the horizontal axis, goes up and to the right, changes direction over approximately 0 on the horizontal axis, and then goes down and to the right before exiting the window just above the horizontal axis. The area under the curve between4 and1.65 as well as the area under the curve between 1.65 and 4 are both shaded.

A plot of the Student's t-probability curve has a horizontal axis with values from4 to 4. The curve enters the window from the left, just above the horizontal axis, goes up and to the right, changes direction over approximately 0 on the horizontal axis, and then goes down and to the right before exiting the window just above the horizontal axis. The area under the curve between1.65 and 4 is shaded.

A plot of the Student's t-probability curve has a horizontal axis with values from4 to 4. The curve enters the window from the left, just above the horizontal axis, goes up and to the right, changes direction over approximately 0 on the horizontal axis, and then goes down and to the right before exiting the window just above the horizontal axis. The area under the curve between 1.65 and 4 is shaded.

A plot of the Student's t-probability curve has a horizontal axis with values from4 to 4. The curve enters the window from the left, just above the horizontal axis, goes up and to the right, changes direction over approximately 0 on the horizontal axis, and then goes down and to the right before exiting the window just above the horizontal axis. The area under the curve between4 and 1.65 is shaded.

(iv)

Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level?

At the= 0.01 level, we reject the null hypothesis and conclude the data are statistically significant.At the= 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant. At the= 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant.At the= 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.

(v)

Interpret your conclusion in the context of the application.

There is sufficient evidence at the 0.01 level to conclude that the population average HC for this patient is higher than 14.There is insufficient evidence at the 0.01 level to conclude that the population average HC for this patient is higher than 14.

9.

[-/0.27 Points]DETAILSBBUNDERSTAT12 8.2.019.S.

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Snow avalanches can be a real problem for travelers in the western United States and Canada. A very common type of avalanche is called the slab avalanche. These have been studied extensively by David McClung, a professor of civil engineering at the University of British Columbia. Suppose slab avalanches studied in a region of Canada had an average thickness of=66cm. The ski patrol at Vail, Colorado, is studying slab avalanches in its region. A random sample of avalanches in spring gave the following thicknesses (in cm).

59	51	76	38	65	54	49	62
68	55	64	67	63	74	65	79

(i) Use a calculator with sample mean and standard deviation keys to findxands. (Round your answers to two decimal places.)

x	=	cm
s	=	cm

(ii) Assume the slab thickness has an approximately normal distribution. Use a 1% level of significance to test the claim that the mean slab thickness in the Vail region is different from that in the region of Canada.(a) What is the level of significance? State the null and alternate hypotheses.H₀:< 66;H₁:= 66H₀:= 66;H₁:66 H₀:= 66;H₁:< 66H₀:66;H₁:= 66H₀:= 66;H₁:> 66

(b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution.The standard normal, since we assume thatxhas a normal distribution andis unknown.The Student'st, since we assume thatxhas a normal distribution andis unknown. The standard normal, since we assume thatxhas a normal distribution andis known.The Student'st, since we assume thatxhas a normal distribution andis known.

What is the value of the sample test statistic? (Round your answer to three decimal places.) (c) Estimate theP-value. P-value > 0.2500.100 <P-value < 0.250 0.050 <P-value < 0.1000.010 <P-value < 0.050P-value < 0.010

Sketch the sampling distribution and show the area corresponding to theP-value.