Question

For the 2015 General Social Survey, a comparison of females and males on the number of hours a day that the subject watched TV gave the following results.

Group	n	Mean
Females	500	3.09
Males	401	2.88

(a) Set up the hypotheses of a significance test to analyze whether the population means differ for females and males.

Ho:   1    ---Select---  =  not equal  >  <   2

Ha:   1    ---Select---  =  not equal  >  <   2

(b) Conduct all parts of the significance test if df = 499 and standard error = 0.163 . Interpret the P-value, and report the conclusion for α = 0.05.

t	=  (3 decimal places, positive value)
P-value	=  (3 decimal places)

(c) Conclusion

There is evidence that females, on average, watch more TV than males.There is not enough evidence to conclude that there is a gender difference in TV watching.    There is evidence to conclude that there is a gender difference in TV watching.

(d) If you were to construct a 95% confidence interval comparing the means, would it contain 0?

No, because according to the test 0 is a plausible value for the difference between the population means.Yes, because according to the test 0 is not a plausible value for the difference between the population means.    Yes, because according to the test 0 is a plausible value for the difference between the population means.No, because according to the test 0 is not a plausible value for the difference between the population means.

Answer 1

a)

b) The test statistic is

   

  

P-value = 2 * P(T > 1.288)

            = 2 * (1 - P(T < 1.288))

            = 2 * (1 - 0.9008)

            = 0.1984

c) Since the P-value is greater than = 0.05, so we should not reject the null hypothesis.

There is not enough evidence to conclude that there is a gender difference in TV watching.

d) Yes, because according to the test 0 is a plausible value for the difference between the population means.