Question

Suppose students' ages follow a skewed right distribution with a mean of 21 years old and a

standard deviation of 2 years. If we randomly sample 450 students, which of the following statements about the sampling distribution of the sample mean age is incorrect?
Select one:
O a.
b . • c.
• d. • e.
Al of the other statements are incorrect
The standard deviation of the sampling distribution is equal to 2 years. The shape of the sampling distribution is approximately normal.
The mean of the sampling distribution is approximately 21 years old. Al of the other statements are correct.

Answer 1

The statement about the sampling distribution of the sample mean age is incorrect is: d. The standard deviation of the sampling distribution is equal to 2 years.

Standard Error: The standard deviation of the sampling distribution, also known as the standard error, is related to the population standard deviation and the sample size.

It is calculated as: Standard Error = Population Standard Deviation / √Sample Size

In this case, the population standard deviation is 2 years and the sample size is 450. Plugging these values into the formula:

Standard Error = 2 years / √450

≈ 0.089 years

Therefore, the standard deviation of the sampling distribution is approximately 0.089 years, much smaller than the population standard deviation of 2 years.