Preview - Sampling Distributions 2021

Another difference of sample means problem

The heights of young men follow a Normal distribution with mean \(\mu_M\)= 69.3 inches and standard deviation \(\sigma_M \)= 2.8 inches. The heights of young women follow a Normal distribution with mean \(\mu_W\) = 64.5 inches and standard deviation \(\sigma_W\) = 2.5 inches. Suppose we select independent SRSs of 16 young men and 9 young women and calculate the sample mean heights \(\bar x_M\) and \(\bar x_W\).

Questions

Please answer the questions below.

What is the shape of the sampling distribution of \(\bar x_M - \bar x_W\)? Why?

Find the mean and standard deviation of the sampling distribution of \(\bar x_M - \bar x_W\)

Calculate the probability that the average height of the 16 randomly selected men is less than the average height of the 9 randomly selected women.

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Notes

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