In a study done by the Scottish government, the average weekly earnings for men were found to be substantially higher than for women. Specifically, the average gross individual weekly income for a random sample of men was £ 317; for a random sample of women, it was £ 172 (source: Social Focus on Men and Women, scotland.gov.uk). If the samples included 1500 men and 1200 women, and the sample standard deviations were £ 89 for the men and £ 67 for the women,

a. Build a 95% confidence interval estimate of the difference in average incomes for the population of Scottish men and the population of Scottish women. 

b. Interpret the interval.