Question

1- From the 2008 General Social Survey, females and males were asked about the number of hours a day that the subject watched TV. Females (n = 698) reported a mean of 3.08 hours with a standard deviation of 2.70 hours. Males (n = 626) reported a mean of 2.87 hours with a standard deviation of 2.61 hours. Test that the mean hours of TV watched by men and women is different from zero at the 5% significance level.

(A) What are the null and alternative hypotheses?

(B) Based on the significance level at which you are testing, what is (are) the critical value(s) for the test?

a) it is a two-sided test. Thus, the tcritis ±1.960.

b) it is a two-sided test. Thus, the tcrit is ±1.645.

c) A one-sided-test with tcrit = 1.96

d) A one-sided test with tcrit = -1.96

(C.1) Calculate the appropriate test statistic. What is the standard error you calculated?

(C.2) Calculate the appropriate test statistic. What is the test statistic you calculated?

(D) Calculate the corresponding p-value from the appropriate table or online calculator.

(E) What conclusions can you draw from the hypothesis test? Be sure to comment on evidence from both the test statistic and p-value.

(F.1) Construct a 95% confidence interval around the difference-in-means estimate. Find the lower bound of the interval you calculated. (In this case, be sure to use the standard error you calculated when determining the test statistic that uses information about the population proportion.)

(F.2) Construct a 95% confidence interval around the difference-in-means estimate. Find the upper bound of the interval you calculated. (In this case, be sure to use the standard error you calculated when determining the test statistic that uses information about the population proportion.)

(G) How would you interpret the confidence interval?

a) We can be 95% confident that the true mean difference in hours of TV watched per week by males and females in the population falls between lower bound and upper bound.

b) We can not be 95% confident that the true mean difference in hours of TV watched per week by males and females in the population falls between lower bound and upper bound.

Answer 1

(g) We can be 95% confident that the true mean difference in hours of TV watched per week by males and females in the population falls between lower bound and upper bound.