Question

Suppose students' ages follow a skewed right distribution with a mean of 24 years old and a standard deviation of 5 years. If we randomly sample 250 students, which of the following statements about the sampling distribution of the sample mean age is incorrect?

		The shape of the sampling distribution is approximately normal.
		The mean of the sampling distribution is approximately 24 years old.
		The standard deviation of the sampling distribution is equal to 5 years.
		All of the above statements are correct.

Answer 1

solution:

sample size,n=250

population mean,=24

=5

When sample size is sufficiently large(i.e. n>=30,then sampling distribution of sample means follow normal distribution with mean equals to population mean and standard deviatition equals to /sqrt(n)

Sampling distribution of sample mean age:

mean=24

standard deviation=5/sqrt(250)

So,incorrect option is:

The standard deviation of the sampling distribution is equal to 5 years