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31 July, 06:34

A university with a high water bill is interested in estimating the mean amount of time that students spend in the shower each day. In a sample of 12 students, the average time was 4.75 minutes and the standard deviation was 1.26 minutes. Using this sample information, construct a 99% confidence interval for the mean amount of time that students spend in the shower each day. Assume normality.

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  1. 31 July, 09:52
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    Step-by-step explanation:

    We want to determine a 99% confidence interval for the mean amount of time that students spend in the shower each day.

    Number of sample, n = 12

    Mean, u = 4.75 minutes

    Standard deviation, s = 1.26 minutes

    For a confidence level of 99%, the corresponding z value is 2.58. This is determined from the normal distribution table.

    We will apply the formula

    Confidence interval

    = mean ± z * standard deviation/√n

    It becomes

    4.75 ± 2.58 * 1.26/√12

    = 4.75 ± 2.58 * 0.364

    = 4.75 ± 0.939

    The lower end of the confidence interval is 4.75 - 0.939 = 3.811

    The upper end of the confidence interval is 4.75 + 0.939 = 5.689

    Therefore, with 99% confidence interval, the mean amount of time that students spend in the shower each day is between 3.811 minutes and 5.689 minutes
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