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 504 3.07 Males 398 2.87 (a) Set up the hypotheses of a significance test to analyze whether the population means differ for females and males. Ho: 1 Correct: Your answer is correct. 2 Ha: 1 Correct: Your answer is correct. 2 (b) Conduct all parts of the significance test if df = 503 and standard error = 0.162 . 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 evidence to conclude that there is a gender difference in TV watching. There is not enough 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 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. No, because according to the test 0 is not a plausible value for the difference between the population means.

Answer 1

a) H₀:

    H₁:

b) The test statistic t = ()/SE

                                  = (3.07 - 2.87)/0.162 = 1.235

P-value = 2 * P(T > 1.235)

            = 2 * (1 - P(T < 1.235))

           = 2 * (1 - 0.8913)

          = 2 * 0.1087 = 0.2174 = 0.217

At alpha = 0.05, the critical values are t^* = +/- 1.965

c) Since the P-value is greater than the significance level(0.217 > 0.05), so we should not reject H₀.

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.