3. university dean of students wishes to estimate the average number of hours students spend doing homework per week. The standard deviation

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3. university dean of students wishes to estimate the average number of hours students spend doing homework per week. The standard deviation from a previous study is 4 hours. How large a sample must be selected if he wants to be 96% confident of finding whether the true mean differs from the sample mean by 2 hours

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Lệ Thu 4 years 2021-08-03T17:48:15+00:00 1 Answers 23 views 0

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  1. quangkhai
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    2021-08-03T17:49:52+00:00
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    Answer:

    A sample of 17 must be selected.

    Step-by-step explanation:

    We have that to find our \alpha level, that is the subtraction of 1 by the confidence interval divided by 2. So:

    \alpha = \frac{1 - 0.96}{2} = 0.02

    Now, we have to find z in the Z-table as such z has a p-value of 1 - \alpha.

    That is z with a pvalue of 1 - 0.02 = 0.98, so Z = 2.054.

    Now, find the margin of error M as such

    M = z\frac{\sigma}{\sqrt{n}}

    In which \sigma is the standard deviation of the population and n is the size of the sample.

    The standard deviation from a previous study is 4 hours.

    This means that \sigma = 4

    How large a sample must be selected if he wants to be 96% confident of finding whether the true mean differs from the sample mean by 2 hours?

    A sample of n is required.

    n is found for M = 2. So

    M = z\frac{\sigma}{\sqrt{n}}

    2 = 2.054\frac{4}{\sqrt{n}}

    2\sqrt{n} = 2.054*4

    Simplifying both sides by 2:

    \sqrt{n} = 2.054*2

    (\sqrt{n})^2 = (2.054*2)^2

    n = 16.88

    Rounding up:

    A sample of 17 must be selected.

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