According to an estimate, the average earnings of female workers who are not union members are $909 per week and those of female workers who are union members are $1035 per week. Suppose that these average earnings are calculated based on random samples of 1500 female workers who are not union members and 2000 female workers who are union members. Further assume that the standard deviations for the two corresponding populations are $70 and $90, respectively.
a. Construct a 95% confidence interval for the difference between the two population means.
b. Test at a 2.5% significance level whether the mean weekly earnings of female workers who are not union members are less than those of female workers who are union members.