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Chapter 7: Problem 29

A population has a distribution that is skewed to the right. A sample of size \(n\) is selected from this population. Describe the shape of the sampling distribution of the sample mean for each of the following cases. a. \(n=25\) b. \(n=80\) c. \(n=29\)

Short Answer

Expert verified
For a right-skewed population, if the sample size is not large (as with n=25 and n=29), the sampling distribution will be skewed to the right, mirroring the population. However, if the sample size is large (as with n=80), thanks to the Central Limit Theorem, the distribution is expected to be approximately normal.

Step by step solution

01

Sample Size: n=25

When the sample size is 25, it is not sufficiently large for the Central Limit Theorem to hold, and the distribution of the population is skewed to the right. This means that the sampling distribution of the sample mean may also be somewhat skewed to the right.
02

Sample Size: n=80

When the sample size is 80, it is sufficiently large for the Central Limit Theorem to come into effect. As per the theorem, the shape of the sampling distribution of the sample mean will be approximately normally distributed, regardless of the shape of the population distribution.
03

Sample Size: n=29

When the sample size is 29, it is generally not large enough for the Central Limit Theorem to hold, so the shape of the sampling distribution will likely mirror the skew of the population, which is skewed to the right.

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