the physiological changes that accompany laughter, statistics homework help

1. Researchers investigated the physiological changes that accompany laughter. Ninety subjects (18-34 years old) watched film clips designed to evoke laughter. During the laughing period, the researchers measured the heart rate (beats per minute) of each subject, with the following summary results: x=73.3, s=5. It is well known that the mean resting heart rate of adults is 71 beats per minute. Complete parts a through d below.

a. Set up Upper H 0and Upper H Subscript a for testing whether the true mean heart rate during laughter exceeds 71 beats per minute. Choose the correct answer below.

A.

H 0: μ=71

H a: μ <71

B.

H 0: μ=71

H a: μ >71

C.

H 0: μ=71

H a: μ ≠71

D.

H 0: μ ≠71

H a: μ=71

2. A business journal investigation of the performance and timing of corporate acquisitions discovered that in a random sample of 2,962 firms, 662 announced one or more acquisitions during the year 2000. Does the sample provide sufficient evidence to indicate that the true percentage of all firms that announced one or more acquisitions during the year 2000 is less than 24%? Use alphaαequals=0.10 to make your decision.

What are the hypotheses for this test?

A.

H 0 : p=0.24

H a: p<0.24

B.

H0: >0.24

Ha: p≤0.24

C.

H0: p≠0.24

Ha: p=0.24

D.

H0: p=0.24

Ha: p≠0.24

E.

H0: p=0.24

Ha: p>0.24

F.

H0: p<0.24

Ha: p=0.24

What is the rejection region?

What is the conclusion of the test?

a.Do not reject or Reject

the null hypothesis because the test statistic

b. Is or is not

in the rejection region. Therefore, there is

c. Insufficient or sufficient evidence at the 0.10 level of significance to indicate that the true percentage of all firms that announced one or more acquisitions during the year 2000 is less than 24%.

3. In a test of H0: μ=10 versus Ha: μ≠10, a sample of n=50 observations possessed mean x=10.8 and a standard deviation s= 3.1 Find and interpret the p-value for the test.

The p-value is p= ________(Round to four decimal places as needed.)

Interpret the result. Choose the correct answer below.

A.There is insufficient evidence to reject H 0 for a= 0.15.

B.There is sufficient evidence to reject H 0 for a= > 0.07.

C.There is sufficient evidence to reject H 0 for a= <0.07.