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[Steps Shown] A Cornell University study of wage differentials between men and women reported that one of the reasons wages for men are higher than wages

Question: A Cornell University study of wage differentials between men and women reported that one of the reasons wages for men are higher than wages for women is that men tend to have more years of work experience than women. Assume the following results were obtained for each group.

\[\begin{array}{cc} \text { Men } & \text { Women } \\ n_{1}=100 & n_{2}=85 \\ \tilde{x}_{1}=14.9 \text { years } & \vec{x}_{2}=10.3 \text { years } \\ \sigma_{1}=5.2 \text { years } & \sigma_{2}=3.8 \text { years } \end{array}\]
  1. What is the point estimate of the difference between the two population means?
  2. At \(95 \%\) confidence, what is the margin of error?
  3. What is the \(95 \%\) confidence interval estimate of the difference between the two population means?

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