Question

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.

n 1 = n m a l e s = 626

n 2 = n f e m a l e s = 698

x ¯ 1 = x ¯ m a l e s = 2.87

x ¯ 2 = x ¯ f e m a l e s = 3.08

S x ¯ 1 = S x ¯ m a l e s = 2.61

S x ¯ 2 = S x ¯ fem a l e s = 2.70

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

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

(B) Calculate the corresponding p-value from the appropriate table.

a) P value is bigger than 0.05

b) P value is smaller than 0.05

c) P value is smaller than 0.001

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

(D.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.)

(D.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.)

(E) How would you interpret the confidence interval?

(F) What connections can you draw between the confidence interval and the hypothesis test?

Answer 1

(e) 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.

(f) from hypothesis test and confidence interval we fail to reject the null hypothesis.