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19 November, 05:51

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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  1. 19 November, 06:12
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    The question is incomplete! Complete question along with answer and step by step explanation is provided below.

    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?

    Answer:

    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.
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