10.86 How often do you feel sad? A recent General Social Survey asked, “How many days in the past seven days have you felt sad?” Software comparing results for men and women who responded showed the following results.

a. Explain how to interpret the P-value. Do you think that the population means may be equal? Why?

b. Explain how to interpret the confidence interval for the difference between the population means. What do you learn from the confidence interval that you cannot learn from the test?

c. What assumptions are made for these inferences?
Can you tell from the summary statistics shown whether any of the assumptions is seriously violated?
What’s the effect?

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Gender N Mean StDev SE Mean Female 816 1.81 1.98 0.069 Male 633 1.42 1.83 0.073 Difference (Female) - (Male) Estimate for difference: 0.390 95% CI for difference: (0.193, 0.587) T-Test of difference = 0 (vs): - T-Value = 3.88 P-Value = 0.000 DF = 1403