2. 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).

95

90

82

107

97

112

84

91

The sample mean isx94.8. 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; right-tailed

H₀:= 85;H₁:85; two-tailed

H₀:= 85;H₁:< 85; left-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, sincenis large with unknown. The standard normal, since we assume thatxhas a normal distribution with unknown.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.

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 2.21 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)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.

3. 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 of39waves showed an average wave height ofx=17.3feet. 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 unknown.The Student'st, since the sample size is large andis known. The Student'st, since the sample size is large andis unknown.The standard normal, since the sample size is large andis known.

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.

4.

[-/4.08 Points]DETAILSBBUNDERSTAT12 8.2.012.MI.S.

MY NOTES

ASK YOUR TEACHER

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 of36patients with arthritis took the drug for 3 months. Blood tests showed thatx=8.8with sample standard deviations=3.3.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 unknown.The Student'st, since the sample size is large andis known. The Student'st, since the sample size is large andis unknown.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 > 0.1000.050 <P-value < 0.100 0.020 <P-value < 0.0500.010 <P-value < 0.020P-value < 0.010

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 and2.55 as well as the area under the curve between 2.55 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 and2.55 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 between2.55 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 2.55 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.

5.

[-/4.08 Points]DETAILSBBUNDERSTAT12 8.2.013.S.

MY NOTES

ASK YOUR TEACHER

A random sample of46adult coyotes in a region of northern Minnesota showed the average age to bex=2.03years, with sample standard deviations=0.76years. 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 standard normal, since the sample size is large andis known.The Student'st, since the sample size is large andis known. The Student'st, since the sample size is large andis unknown.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.

6.

[-/4.08 Points]DETAILSBBUNDERSTAT12 8.2.014.MI.S.

MY NOTES

ASK YOUR TEACHER

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=2.9inches. 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 in H₀:= 19 in;H₁:> 19 in H₀:= 19 in;H₁:19 in H₀:= 19 in;H₁:< 19 in H₀:> 19 in;H₁:= 19 in

(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 known.The Student'st, since the sample size is large andis unknown. The standard normal, since the sample size is large andis unknown.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 > 0.0100.0010 <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 between0.99 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 and0.99 as well as the area under the curve between 0.99 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 0.99 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 and0.99 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.

7.

[-/4.08 Points]DETAILSBBUNDERSTAT12 8.3.009.S.

MY NOTES

ASK YOUR TEACHER

Is the national crime rate really going down? Some sociologists say yes! They say that the reason for the decline in crime rates in the 1980s and 1990s is demographics. It seems that the population is aging, and older people commit fewer crimes. According to the FBI and the Justice Department, 70% of all arrests are of males aged 15 to 34 years. Suppose you are a sociologist in Rock Springs, Wyoming, and a random sample of police files showed that of36arrests last month,28were of males aged 15 to 34 years. Use a10%level of significance to test the claim that the population proportion of such arrests in Rock Springs is different from 70%.

(a) What is the level of significance? State the null and alternate hypotheses. H₀:p= 0.7;H₁:p0.7H₀:p< 0 .7;H₁:p= 0.7 H₀:p0.7;H₁:p= 0.7H₀:p= 0 .7;H₁:p< 0.7H₀:p= 0.7;H₁:p> 0.7

(b) What sampling distribution will you use? The standard normal, sincenp> 5 andnq> 5.The Student'st, sincenp> 5 andnq> 5. The standard normal, sincenp< 5 andnq< 5.The Student'st, sincenp< 5 andnq< 5.

What is the value of the sample test statistic? (Round your answer to two decimal places.) (c) Find theP-value of the test statistic. (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= 0.10 level, we reject the null hypothesis and conclude the data are statistically significant.At the= 0.10 level, we reject the null hypothesis and conclude the data are not statistically significant. At the= 0.10 level, we fail to reject the null hypothesis and conclude the data are statistically significant.At the= 0.10 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 0.10 level to conclude that the true proportion of arrests of males aged 15 to 34 in Rock Springs differs from 70%.There is insufficient evidence at the 0.10 level to conclude that the true proportion of arrests of males aged 15 to 34 in Rock Springs differs from 70%.

8.

[-/4.08 Points]DETAILSBBUNDERSTAT12 8.3.010.MI.S.

MY NOTES

ASK YOUR TEACHER

Women athletes at a certain university have a long-term graduation rate of 67%. Over the past several years, a random sample of38women athletes at the school showed that21eventually graduated. Does this indicate that the population proportion of women athletes who graduate from the university is now less than 67%? Use a1% level of significance.

(a)

What is the level of significance?

(b)

State the null and alternate hypotheses.

H₀:p= 0.67;H₁:p< 0.67H₀:p= 0.67;H₁:p0.67 H₀:p= 0.67;H₁:p> 0.67H₀:p< 0.67;H₁:p= 0.67

What sampling distribution will you use?

The Student'st, sincenp> 5 andnq> 5.The standard normal, sincenp< 5 andnq< 5. The Student'st, sincenp< 5 andnq< 5.The standard normal, sincenp> 5 andnq> 5.

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

(c)

Find theP-value of the test statistic. (Round your answer to four decimal places.)

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

A plot of the standard 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 and1.54 as well as the area under the curve between 1.54 and 3 are both shaded.

A plot of the standard 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 1.54 and 3 is shaded.

A plot of the standard 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 between1.54 and 3 is shaded.

A plot of the standard 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 and1.54 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 true proportion of women athletes who graduate is less than 0.67.There is insufficient evidence at the 0.01 level to conclude that the true proportion of women athletes who graduate is less than 0.67.

9.

[-/4.08 Points]DETAILSBBUNDERSTAT12 8.4.009.MI.S.

MY NOTES

ASK YOUR TEACHER

In this problem, assume that the distribution of differences is approximately normal.Note: For degrees of freedomd.f. not in the Student'sttable, use the closestd.f. that issmaller. In some situations, this choice ofd.f. may increase theP-value by a small amount and therefore produce a slightly more "conservative" answer.

Are America's top chief executive officers (CEOs) really worth all that money? One way to answer this question is to look at rowB, the annual company percentage increase in revenue, versus rowA, the CEO's annual percentage salary increase in that same company. Suppose a random sample of companies yielded the following data:

B: Percent increase for company	24	25	27	18	6	4	21	37
A: Percent increase for CEO	25	23	22	14	4	19	15	30

Do these data indicate that the population mean percentage increase in corporate revenue (rowB) is different from the population mean percentage increase in CEO salary? Use a 5% level of significance. (Letd=BA.)

(a)

What is the level of significance?

State the null and alternate hypotheses.

H₀:_d0;H₁:_d= 0H₀:_d= 0;H₁:_d0 H₀:_d= 0;H₁:_d< 0H₀:_d= 0;H₁:_d> 0H₀:_d> 0;H₁:_d= 0

(b)

What sampling distribution will you use? What assumptions are you making?

The Student'st. We assume thatdhas an approximately normal distribution.The standard normal. We assume thatdhas an approximately uniform distribution. The standard normal. We assume thatdhas an approximately normal distribution.The Student'st. We assume thatdhas an approximately uniform distribution.

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

(c)

Find (or estimate) theP-value.

P-value > 0.5000.250 <P-value < 0.500 0.100 <P-value < 0.2500.050 <P-value < 0.1000.010 <P-value < 0.050P-value < 0.010

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

A plot of the sampling distribution 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 0.826 and 4 is shaded.

A plot of the sampling distribution 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 and0.826 as well as the area under the curve between 0.826 and 4 are both shaded.

A plot of the sampling distribution 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 between0.826 and 4 is shaded.

A plot of the sampling distribution 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 and0.826 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?

Since theP-value >, we rejectH₀. The data are not statistically significant.Since theP-value, we rejectH₀. The data are statistically significant. Since theP-value >, we fail to rejectH₀. The data are not statistically significant.Since theP-value, we fail to rejectH₀. The data are statistically significant.

(e)

Interpret your conclusion in the context of the application.

Fail to rejectH₀. At the 5% level of significance, the evidence is insufficient to claim a difference in population mean percentage increases for corporate revenue and CEO salary.RejectH₀. At the 5% level of significance, the evidence is sufficient to claim a difference in population mean percentage increases for corporate revenue and CEO salary. Fail to rejectH₀. At the 5% level of significance, the evidence is sufficient to claim a difference in population mean percentage increases for corporate revenue and CEO salary.RejectH₀. At the 5% level of significance, the evidence is insufficient to claim a difference in population mean percentage increases for corporate revenue and CEO salary.

10.

[-/4.08 Points]DETAILSBBUNDERSTAT12 8.4.010.S.

MY NOTES

ASK YOUR TEACHER

In this problem, assume that the distribution of differences is approximately normal.Note: For degrees of freedomd.f. not in the Student'sttable, use the closestd.f. that issmaller. In some situations, this choice ofd.f. may increase theP-value by a small amount and therefore produce a slightly more "conservative" answer. Is fishing better from a boat or from the shore? Pyramid Lake is located on the Paiute Indian Reservation in Nevada. Presidents, movie stars, and people who just want to catch fish go to Pyramid Lake for really large cutthroat trout. Let rowBrepresent hours per fish caught fishing from the shore, and let rowArepresent hours per fish caught using a boat. The following data are paired by month from October through April.

	Oct	Nov	Dec	Jan	Feb	March	April
B: Shore	1.4	1.9	2.1	3.2	3.9	3.6	3.3
A: Boat	1.4	1.5	1.5	2.2	3.3	3.0	3.8

Use a 1% level of significance to test if there is a difference in the population mean hours per fish caught using a boat compared with fishing from the shore. (Letd=BA.)(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:_d= 0;H₁:_d< 0; left-tailedH₀:_d= 0;H₁:_d> 0; right-tailed H₀:_d0;H₁:_d= 0; two-tailedH₀:_d= 0;H₁:_d0; two-tailed

(b) What sampling distribution will you use? What assumptions are you making? The standard normal. We assume thatdhas an approximately uniform distribution.The standard normal. We assume thatdhas an approximately normal distribution. The Student'st. We assume thatdhas an approximately uniform distribution.The Student'st. We assume thatdhas an approximately normal distribution.

What is the value of the sample test statistic? (Round your answer to three decimal places.) (c) Find (or estimate) theP-value. P-value > 0.5000.250 <P-value < 0.500 0.100 <P-value < 0.2500.050 <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 fail to 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 reject the null hypothesis and conclude the data are not statistically significant.At the= 0.01 level, we reject the null hypothesis and conclude the data are statistically significant.

(e) State your conclusion in the context of the application. Reject the null hypothesis, there is sufficient evidence to claim a difference in population mean hours per fish between boat fishing and shore fishing.Fail to reject the null hypothesis, there is insufficient evidence to claim a difference in population mean hours per fish between boat fishing and shore fishing. Fail to reject the null hypothesis, there is sufficient evidence to claim a difference in population mean hours per fish between boat fishing and shore fishing.Reject the null hypothesis, there is insufficient evidence to claim a difference in population mean hours per fish between boat fishing and shore fishing.

11.

[-/4.08 Points]DETAILSBBUNDERSTAT12 8.5.013.MI.S.

MY NOTES

ASK YOUR TEACHER

For one binomial experiment,

n₁= 75

binomial trials produced

r₁=45

successes. For a second independent binomial experiment,

n₂= 100

binomial trials produced

r₂=65

successes.At the 5% level of significance, test the claim that the probabilities of success for the two binomial experiments differ.

(a)

Compute the pooled probability of success for the two experiments. (Round your answer to three decimal places.)

(b)

Check Requirements: What distribution does the sample test statistic follow? Explain.

The standard normal. We assume the population distributions are approximately normal.The Student'st. The number of trials is sufficiently large. The standard normal. The number of trials is sufficiently large.The Student'st. We assume the population distributions are approximately normal.

(c)

State the hypotheses.

H₀:p₁=p₂;H₁:p₁<p₂H₀:p₁=p₂;H₁:p₁p₂ H₀:p₁<p₂;H₁:p₁=p₂H₀:p₁=p₂;H₁:p₁>p₂

(d)

Computep₁p₂.

p₁p₂=

Compute the corresponding sample distribution value. (Test the differencep₁p₂. Do not use rounded values. Round your final answer to two decimal places.)

(e)

Find theP-value of the sample test statistic. (Round your answer to four decimal places.)

(f)

Conclude the test.

At the= 0.05 level, we 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. 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.

(g)

Interpret the results.

Fail to reject the null hypothesis, there is sufficient evidence that the proportion of the probabilities of success for the two binomial experiments differ.Fail to reject the null hypothesis, there is insufficient evidence that the probabilities of success for the two binomial experiments differ. Reject the null hypothesis, there is sufficient evidence that the proportion of the probabilities of success for the two binomial experiments differ.Reject the null hypothesis, there is insufficient evidence that the proportion of the probabilities of success for the two binomial experiments differ.

12.

[-/4.08 Points]DETAILSBBUNDERSTAT12 8.5.015.

MY NOTES

ASK YOUR TEACHER

REM (rapid eye movement) sleep is sleep during which most dreams occur. Each night a person has both REM and non-REM sleep. However, it is thought that children have more REM sleep than adults. Assume that REM sleep time is normally distributed for both children and adults. A random sample ofn₁=8children (9 years old) showed that they had an average REM sleep time ofx₁=2.5hours per night. From previous studies, it is known that₁=0.6hour. Another random sample ofn₂=8adults showed that they had an average REM sleep time ofx₂=1.70hours per night. Previous studies show that₂=0.7hour. Do these data indicate that, on average, children tend to have more REM sleep than adults? Use a 1% level of significance.(a) What is the level of significance? State the null and alternate hypotheses. H₀:₁=₂;H₁:₁>₂H₀:₁=₂;H₁:₁<₂ H₀:₁<₂;H₁:₁=₂H₀:₁=₂;H₁:₁₂

(b) What sampling distribution will you use? What assumptions are you making? The standard normal. We assume that both population distributions are approximately normal with known standard deviations.The Student'st. We assume that both population distributions are approximately normal with unknown standard deviations. The standard normal. We assume that both population distributions are approximately normal with unknown standard deviations.The Student'st. We assume that both population distributions are approximately normal with known standard deviations.

What is the value of the sample test statistic? (Test the difference₁₂. 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 fail to reject the null hypothesis and conclude the data are not 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.

(e) Interpret your conclusion in the context of the application. Fail to reject the null hypothesis, there is insufficient evidence that the mean REM sleep time for children is more than for adults.Fail to reject the null hypothesis, there is sufficient evidence that the mean REM sleep time for children is more than for adults. Reject the null hypothesis, there is insufficient evidence that the mean REM sleep time for children is more than for adults.Reject the null hypothesis, there is sufficient evidence that the mean REM sleep time for children is more than for adults.

13.

[-/4.17 Points]DETAILSBBUNDERSTAT12 8.5.020.S.

MY NOTES

ASK YOUR TEACHER

A random sample ofn₁= 16 communities in western Kansas gave the following information for people under 25 years of age.x₁: Rate of hay fever per 1000 population for people under 25

100	92	122	129	91	123	112	93
125	95	125	117	97	122	127	88

A random sample ofn₂= 14 regions in western Kansas gave the following information for people over 50 years old.x₂: Rate of hay fever per 1000 population for people over 50

94	109	99	99	110	88	110
79	115	100	89	114	85	96

(i) Use a calculator to calculatex₁,s₁,x₂, ands₂. (Round your answers to four decimal places.)

x1	=
s1	=
x2	=
s2	=

(ii) Assume that the hay fever rate in each age group has an approximately normal distribution. Do the data indicate that the age group over 50 has a lower rate of hay fever? Use= 0.05. (a) What is the level of significance? State the null and alternate hypotheses. H₀:₁=₂;H₁:₁>₂H₀:₁=₂;H₁:₁<₂ H₀:₁>₂;H₁:₁=₂H₀:₁=₂;H₁:₁₂

(b) What sampling distribution will you use? What assumptions are you making? The standard normal. We assume that both population distributions are approximately normal with unknown standard deviations.The standard normal. We assume that both population distributions are approximately normal with known standard deviations. The Student'st. We assume that both population distributions are approximately normal with known standard deviations.The Student'st. We assume that both population distributions are approximately normal with unknown standard deviations.

What is the value of the sample test statistic? (Test the difference₁₂. Round your answer to three decimal places.) (c) Find (or estimate) theP-value. P-value > 0.2500.125 <P-value < 0.250 0.050 <P-value < 0.1250.025 <P-value < 0.0500.005 <P-value < 0.025P-value < 0.005

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

(e) Interpret your conclusion in the context of the application.

Fail to reject the null hypothesis, there is sufficient evidence that the mean rate of hay fever is lower for the age group over 50.

Reject the null hypothesis, there is sufficient evidence that the mean rate of hay fever is lower for the age group over 50. Reject the null hypothesis, there is insufficient evidence that the mean rate of hay fever is lower for the age group over 50.Fail to reject the null hypothesis, there is insufficient evidence that the mean rate of hay fever is lower for the age group over 50.