A random sample of 100 women from the General Social Survey showed that the mean number of children reported was 1.85 with a standard deviation of 1.5. (Interestingly, a sample of 100 men showed a mean of 1.49 children.)

a. Find a 95% confidence interval for the population mean number of children for women. Because the sample size is so large, you can use 1.96 for the critical value of t (which is the same as the critical value of z) if you do the calculations manually.

b. Find a 90% confidence interval. Use 1.645 for the critical value of t, which is the critical value of z.

c. Which interval is wider, and why?