A professor wants to estimate the average time it takes his students to finish a computer project. Based on previous evidence, he believes t

Question

A professor wants to estimate the average time it takes his students to finish a computer project. Based on previous evidence, he believes that the standard deviation is approximately 3.6 hours. He would like to be 96% confident that his estimate is within 5 hours of the true population mean. Use RStudio to determine how large of a sample size is required without rounding any interim calculations.

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Neala 6 months 2021-08-27T04:30:36+00:00 1 Answers 4 views 0

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    2021-08-27T04:32:22+00:00

    Answer:

    A sample size of 3 is required.

    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.

    Based on previous evidence, he believes that the standard deviation is approximately 3.6 hours.

    This means that \sigma = 3.6

    He would like to be 96% confident that his estimate is within 5 hours of the true population mean. Use RStudio to determine how large of a sample size is required without rounding any interim calculations.

    The sample size needed is of n, and n is found when M = 5. So

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

    5 = 2.054\frac{3.6}{\sqrt{n}}

    5\sqrt{n} = 2.054*3.6

    \sqrt{n} = \frac{2.054*3.6}{5}

    (\sqrt{n})^2 = (\frac{2.054*3.6}{5})^2

    n = 2.19

    Rounding up:

    A sample size of 3 is required.

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