Question

A sociologist is studying the number of years of education of students whose mothers have bachelor's degrees or higher. The data is normally distributed with a population mean of 14.5 years and a population standard deviation of 2.5 years. If a sample of 55 students is selected at random from the population, select the mean and standard deviation of the sampling distribution below.

a. σi= 0.05 years
b. σi= 2.5 years
c. σi= 0.34 years
d. µ= 14.5 years

Answer 1

The mean of the sampling distribution is 14.5 years and the standard deviation is 0.34 years.

Explanation:

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean
`\mu` and standard deviation
`\sigma`, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean
`\mu` and standard deviation
`s = (\sigma)/(√(n))`.

Population:

`\mu = 14.5, \sigma = 2.5`

Sample:

55 students, so
`n = 55`

Then

`\mu = 55, s = (2.5)/(√(55)) = 0.34`

The mean of the sampling distribution is 14.5 years and the standard deviation is 0.34 years.