Question

A researcher wants to estimate the mean number of hours per day that elementary aged school children spend watching TV in order to direct subsequently planned research in reducing time spent watching TV among young children. She collects a sample of 424 children and calculates a 95% confidence interval for number of hours per day spent watching TV: Confidence interval - (1.93, 4.25).

a. (3pts) Interpret this confidence interval in a sentence below.


b. (5pts) Would a two-sided hypothesis test, performed at significance level 0.05, for testing whether mean number of hours per day spent watching TV is equal to 2.5. reject the null hypothesis? How about a test for mean number of hours per day being equal to 1.2? (You need to have two answers for this question. The first is for p = 2.5, and the second is for u = 1.2).

Answer 1

a) The confidence interval (1.93, 4.25) means that there is 95% confidence that the population mean for the number of hours per day spent watching TV is within 1.93 and 4.25.

b) H0: μ=2.5. The null hypothesis failed to be rejected.

H0: μ=1.2. The null hypothesis is rejected.

Explanation:

a) The confidence interval (1.93, 4.25) means that there is 95% confidence that the population mean for the number of hours per day spent watching TV is within 1.93 and 4.25.

b) If a two-sided hypthesis test is performed at a significance level of 0.05 with a null hypothesis H0: μ=2.5, the result would be that the null hypothesis failed to be rejected.

This is because we have the information of the 95% confidence level, that has the same level of significance and is also two-sided, includes the value 2.5. The confidence interval is, in this case, equivalent to the acceptance region for the hypothesis test, so the null hypothesis failed to be rejected.

If the null hypothesis mean would have fallen outside of the limits of the confidecence interval, the null hypothesis would have been rejected.

This is the case of H0: μ=1.2, which lies outside the confidence interval (in the rejection region). Then, the null hypothesis is rejected.