Problem 11.

For each statement, select the correct null hypothesis, H0, and alternative hypothesis, Ha, in symbolic form.

(a) The mean height of all adult American males is 69 inches (5 ft 9 in). A researcher wonders if young American males between the ages of 18 and 21 tend to be taller than 69 inches. A random sample of 100 young American males ages 18 to 21 yielded a sample mean of 71 inches. A. H0:69 , Ha:>69 B. H0:=69, Ha:69 C. H0:>69, Ha:<69 D. H0:x69, Ha:x>69 E. H0:71, Ha:<71 F. H0:x71, Ha:x<71

(b) A certain type of hummingbird is known to have an average weight of 4.55 grams. A researcher wonders if hummingbirds (of this same type) living in the Grand Canyon differ in weight from the population as a whole. The researcher finds a sample of 30 such hummingbirds from the Grand Canyon and calculates their average weight to be 3.75 grams. A. H0:=3.75, Ha:3.75 B. H0:x4.55, Ha:x<4.55 C. H0:<4.55, Ha:=4.55 D. H0:=4.55, Ha:4.55 E. H0:x3.75, Ha:x>3.75 F. H0:4.55, Ha:<4.55

(c) According to the Merck Veterinary Manual, the average resting heart rate for a certain type of sheep dog is 115 beats per minute (bpm). A Montana farmer notices his aging sheep dog has been acting more lethargic than usual and wonders if her heart rate is slowing. He measures her heart rate on 15 occasions and finds a sample mean heart rate of 118.2 bpm. A. H0:=115, Ha:115 B. H0:x=118.2, Ha:x118.2 C. H0:x115 Ha:x>115 D. H0:115, Ha:<115 E. H0:118.2, Ha:<118.2 F. H0:115, Ha:>115

Problem 12.

Suppose that we are to conduct the following hypothesis test:

H0: = 560

H1: 560

Suppose that you also know that for n=16, x=690.1 and s=200. Take =0.05. Determine each of the following:

A. The value of the test statistic:

______________

B. The p-value is ________________

C. Your decision for the hypothesis test: A. Reject H0. B. Reject H1. C. Do Not Reject H0. D. Do Not Reject H1.

Problem 13.

The hypothesis test

H0:p=0.49

H1:p0.49 is to be carried out for a random sample of 180. The test statistic is found to be z=0.32. What was the sample proportion?

p^ = ________________

Problem 14.

Suppose that you are to conduct the following hypothesis test:

H0: 6.1

H1: > 6.1

A sample of 13 was found to have a mean of 7.1 and a standard deviation of 1.08. Determine each of the following:

The value of the test statistic:

For = 0.025, the final conclusion is

A. There is enough evidence to say that 6.1 B. There is enough evidence to say that >6.1 C. There is not enough evidence to say that >6.1 D. There is not enough evidence to say that 6.1

Problem 15.

Select the correct null hypothesis, H0, and alternative hypothesis, Ha, in symbolic form.

A chain of stores specializing in camping gear is considering a promotion that involves mailing out discount coupons. To test this promotion, the chain will first mail discount coupons to residents in a certain area and study the proportion of coupoons that will actually be used. The chain wants to know if the proportion is less than 15% A. H0:p0.15, Ha:p<0.15 B. H0:p=0.15, Ha:p0.15 C. H0:0.15, Ha:>0.15 D. H0:p>0.15, Ha:p0.15 E. H0:15, Ha:>15 F. H0:p0.15, Ha:p>0.15

Problem 16.

Suppose that we reject a null hypothesis at the 0.02 level of significance. Then for which of the following values do we also reject the null hypothesis? A. 0.002 B. 0.01 C. 0.003 D. 0.03 E. 0.001

Problem 17.

A matched pairs experiment is carried out, yielding the following data:

n=18, d=1.2, sd=2.92596

Is there evidence, at an =0.1 level of significance, to conclude that there is a difference between the two sets of measurements? Carry out an appropriate hypothesis test, filling in the information requested.

A. The value of the test statistic: ___________

B. The degree of freedom for the distribution: __________

C. The p-value is approximately____________

D. Your decision for the hypothesis test:_____________ A. Reject H0. B. Do Not Reject H0. C. Reject H1. D. Do Not Reject H1.

Problem 18.

A company that sponsors LSAT prep courses would like to be able to claim that their courses improve scores. To test this, they take a sample of 8 people, have each take an initial diagnostic test, then take the prep course, and then take a post-test after the course. The test results are below (scores are out of 100%):

Person Initial Test Post-Test

1 65 72

2 71 69

3 70 70

4 65 76

5 75 74

6 77 72

7 80 82

8 73 88

Is there evidence, at an =0.01 level of significance, to conclude that the prep course improves scores? Carry out an appropriate hypothesis test, filling in the information requested. (Arrange your data so that the standardized test statistic is for the change from the initial test to the post-test.)

A. The value of the standardized test statistic: ____________________

B. Your decision for the hypothesis test:______________________ A. Reject H0. B. Do Not Reject H0. C. Reject H1. D. Do Not Reject H1.

Problem 19.

Select the correct null hypothesis, H0, and alternative hypothesis, Ha, in symbolic form.

Independent samples are taken from two populations for which 1 and 2 are known. A hypothesis test is conducted to see if the first population mean is less than the second population mean A. H0:12zc, Ha:12B. H0:120, Ha:12>0 C. H0:120, Ha:12<0 D. H0:12=0, Ha:120 E. H0:tc0, Ha:tc<0 F. H0:zc0, Ha:zc<0

Problem 20.

Consider a hypothesis test to decide if the mean yield of cotton in a certain region is less than 1 ton per acre. Identify the type of error, if there is error, in the following situations.

a. "The mean cotton yield in the region is actually not less than 1 ton per acre and the result of the sampling does not lead to the conclusion that the mean cotton yield is less than 1 ton per acre" is a A. Type I error B. Type II error C. Correct decision

b. "The mean cotton yield in the region is actually less than 1 ton per acre and the result of the sampling does not lead to the conclusion that the mean cotton yield is less than 1 ton per acre" is a A. Correct decision B. Type II error C. Type I error