Question

Previously, an organization reported that teenagers spent 4.5 hours per week, on average, on the phone. The organization thinks that, currently, the mean is higher. Fifteen randomly chosen teenagers were asked how many hours per week they spend on the phone. The sample mean was 4.75 hours with a sample standard deviation of 2.0. Conduct a hypothesis test. At a significance level of a = 0.05, what is the correct conclusion?

a. There is enough evidence to conclude that the mean number of hours is more than 4.75

b. There is enough evidence to conclude that the mean number of hours is more than 4.5

c. There is not enough evidence to conclude that the mean number of hours is more than 4.5

d. There is not enough evidence to conclude that the mean number of hours is more than 4.75

Short answer

c. There is not enough evidence to conclude that the mean number of hours is more than 4.5

Step-by-step solution

Find H0 and Ha: We want to test if an Organization Teenagers take more than 4.5 hours per week, on average, on the phone.

$H_0:\mu =4.5;H_a:\mu >4.5$

Compare α and the p-value:Indicate the correct decision (“reject” or “do not reject” the null hypothesis), the reason for it, and write an appropriate conclusion, using complete sentences.

alpha	decision	reason for decision
0.05	Do not reject H0	$p-value<0.05$

Conclusion: There is not enough evidence to conclude that the mean number of hours is more than 4.5