We want to estimate the difference between the mean starting salaries for recent

Question

We want to estimate the difference between the mean starting salaries for recent graduates with mechanical engineering and electrical engineering degrees from the University of Michigan (UM). The following information is available: A random sample of 59 starting salaries for UM mechanical engineering graduates produced a sample of $48, 736 and a standard deviation of $4, 430. A random sample of 30 starting salaries for UM electrical engineering graduates produced a sample mean of $53, 208 and a standard deviation of $4, 286. Please derive a 95% confidence interval for the difference between the true mean salaries.

Explanation / Answer

For 95% confidence interval critical z=1.96

95% CI=(xbar1-xbar2)± 1.96*sqrt(12/n1+22/n2)

=(48736-53208)±1.96*sqrt(44302/59+42862/30)

=(-6377.289332 -2566.710668)

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