Question

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 sam- ple 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.

Answer 1

Given umen = £ 317 Twomen = £ 172 Rmen 1500 n women 1200 Smen = £89 I women £ 65 "То find internal for Ulmen - Mevoren Formula the confidence imen - Twomen I margin of Error. 2 łmen - women 2 t Z* Smen nimen + Suomen nuomen at 95% land, Z = 1.9.6 317-172 I (89)? 1.96 .+ (652 1500 1200 5. 8148 => 145 I -> (139.19 150.81) arounded H > 2 decimal places. b) Interpretation the can say Based on 100 that we sample, we 95% confidence that the for is men average higher weekly earnings the average weekly weekly earnings than women between some where by £ 139.19 and € 150.81

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