In the 2016 General Social Survey, one question was “What is the ideal number of children for a family to have?” Of the 738 men who answered, the mean response was 2.52 with a standard deviation of 0.84. In contrast, of the 867 women who answered, the mean response was 2.63 with a standard deviation of 0.89.A 99% confidence interval for the difference in mean ideal number of children is (−0.22, 0.0048).
a) The interval is estimating μ₁ − μ₂. Which population was chosen as number 1?
b) What would happen if we were to get a 99% confidence interval for μ₂ − μ₁?
c) How meaningful is the true difference in mean ideal number of children?
d) Do you think the distribution of answers to the questions are normally distributed?