The average college major requires 34 credit hours to complete, with a standard deviation of 3 hours. A college's academic advisors conduct a study to see how many credit hours a sample size of 50 students will need to take to complete their majors. They calculate:μx= μ = 34and σx= μ /√n =34/√50=4.81What did they do wrong?

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Question:

The average college major requires 34 credit hours to complete, with a standard deviation of 3 hours. A college's academic advisors conduct a study to see how many credit hours a sample size of 50 students will need to take to complete their majors.

They calculate:

μx = μ = 34

σx = μ/√n = 34/√50 = 4.81

What did they do wrong?

The sample mean will be the same as the population mean

μx = μ = 34

Whereas the standard deviation of the sample would be

σx = σ/√n

σx = 3/√50

σx = 0.424

Therefore, the college's academic advisors wrongly calculated the standard deviation of the sampling distribution.

Step-by-step explanation:

From the given information we know that,

The population mean is

μ = 34 credit hours

The population standard deviation is

σ = 34 credit hours

The college's academic advisors take a sample size of 50 students so

sample size = n = 50

Since the sample size is quite large then according to the central limit theorem,

The sample mean will be the same as the population mean

μx = μ = 34

Whereas the standard deviation of the sample would be

σx = σ/√n

σx = 3/√50

σx = 0.424

Therefore, the college's academic advisors wrongly calculated the standard deviation of the sampling distribution.

step-by-step explanation:

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