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 88 80 107 101 108 86 91

The sample mean isx94.5. 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; right-tailed

H₀:= 85;H₁:> 85; right-tailed

H₀:= 85;H₁:< 85; left-tailed

H₀:= 85;H₁:85; two-tailed

(b)

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

(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.

[-/4.08 Points]

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 of35waves showed an average wave height ofx=16.5feet. 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 ft

H₀:= 16.4 ft;H₁:> 16.4 ft

H₀:= 16.4 ft;H₁:< 16.4 ft

H₀:= 16.4 ft;H₁:16.4 ft

H₀:< 16.4 ft;H₁:= 16.4 ft

(b) What sampling distribution will you use? Explain the rationale for your choice of a 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 > 0.250

0.100 <P-value < 0.250

0.050 <P-value < 0.100

0.010 <P-value < 0.050

P-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]

Letxbe a random variable that represents the pH of arterial plasma (i.e., the 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=8.6with sample standard deviations=2.9.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:> 7.4

H₀:= 7.4;H₁:7.4

H₀:= 7.4;H₁:< 7.4

H₀:> 7.4;H₁:= 7.4

H₀:7.4;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 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.

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

(c)

Estimate theP-value.

P-value > 0.100

0.050 <P-value < 0.100

0.020 <P-value < 0.050

0.010 <P-value < 0.020

P-value < 0.010

(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]

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 yr

H₀:= 1.75 yr;H₁:< 1.75 yr

H₀:> 1.75 yr;H₁:= 1.75 yr

H₀:= 1.75 yr;H₁:1.75 yr

H₀:< 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 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 three decimal places.)

(c) Estimate theP-value.

P-value > 0.250

0.100 <P-value < 0.250

0.050 <P-value < 0.100

0.010 <P-value < 0.050

P-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]

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 of46fish caught, the mean length wasx=18.6inches, with estimated standard deviations=3.3inches. 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 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 > 0.010

0.0010 <P-value < 0.010

0.250 <P-value < 0.0010

0.125 <P-value < 0.250

P-value < 0.125

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 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.