Question

In a study of computer use, 1000 randomly selected Canadian Internet users were asked how much time they spend using the Internet in a typical week. The mean of the sample observations was 12.9 hours.

(a) The sample standard deviation was not reported, but suppose that it was 6 hours. Carry out a hypothesis test with a significance level of 0.05 to decide if there is convincing evidence that the mean time spent using the Internet by Canadians is greater than 12.7 hours. (Use a statistical computer package to calculate the P-value. Round your test statistic to two decimal places and your P-value to three decimal places.)

t= P-value =

State the conclusion in the problem context.

a. Reject H₀. We have convincing evidence that the mean weekly time spent using the Internet by Canadians is greater than 12.7 hours.

b. Do not reject H₀. We do not have convincing evidence that the mean weekly time spent using the Internet by Canadians is greater than 12.7 hours.     

c. Do not reject H₀. We have convincing evidence that the mean weekly time spent using the Internet by Canadians is greater than 12.7 hours.

d. Reject H₀. We do not have convincing evidence that the mean weekly time spent using the Internet by Canadians is greater than 12.7 hours.

(b) Now suppose that the sample standard deviation was 2 hours. Carry out a hypothesis test with a significance level of 0.05 to decide if there is convincing evidence that the mean time spent using the Internet by Canadians is greater than 12.7 hours. (Use a statistical computer package to calculate the P-value. Round your test statistic to two decimal places and your P-value to three decimal places.)

t= P-value =

State the conclusion in the problem context.

a. Reject H₀. We have convincing evidence that the mean weekly time spent using the Internet by Canadians is greater than 12.7 hours.

b. Do not reject H₀. We do not have convincing evidence that the mean weekly time spent using the Internet by Canadians is greater than 12.7 hours.    

c. Reject H₀. We do not have convincing evidence that the mean weekly time spent using the Internet by Canadians is greater than 12.7 hours.

d. Do not reject H₀. We have convincing evidence that the mean weekly time spent using the Internet by Canadians is greater than 12.7 hours.

(c) Explain why the hypothesis tests resulted in different conclusions for part (a) and part (b).

a.The larger standard deviation means that you can expect less variability in measurements and smaller deviations from the mean. This explains why H₀ is rejected when the sample standard deviation is 6, but not when the sample standard deviation is 2.

b. The smaller standard deviation means that you can expect more variability in measurements and greater deviations from the mean. This explains why H₀ is rejected when the sample standard deviation is 2, but not when the sample standard deviation is 6.     

c. The smaller standard deviation means that you can expect less variability in measurements and smaller deviations from the mean. This explains why H₀ is rejected when the sample standard deviation is 6, but not when the sample standard deviation is 2.

d. The larger standard deviation means that you can expect more variability in measurements and greater deviations from the mean. This explains why H₀ is rejected when the sample standard deviation is 2, but not when the sample standard deviation is 6.

Answer 1

(a)

b. Do not reject H₀. We do not have convincing evidence that the mean weekly time spent using the Internet by Canadians is greater than 12.7 hours.

(b)

Correct option:

a. Reject H₀. We have convincing evidence that the mean weekly time spent using the Internet by Canadians is greater than 12.7 hours.

(c)

d. The larger standard deviation means that you can expect more variability in measurements and greater deviations from the mean. This explains why H₀ is rejected when the sample standard deviation is 2, but not when the sample standard deviation is 6.