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9 March, 09:24

In a random sample of 2121 people, the mean commute time to work was 30.130.1 minutes and the standard deviation was 7.17.1 minutes. assume the population is normally distributed and use a t-distribution to construct a 8080 % confidence interval for the population mean muμ. what is the margin of error of muμ ? interpret the results.

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  1. 9 March, 09:40
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    The margin of error can be calculated using the t statistic. The formula for margin of error is given as:

    Margin of error = t * s / sqrt (n) - - - > 1

    Where,

    t = the t score based on the given confidence level and degrees of freedom

    n = number of samples = 21

    s = standard deviation = 7.1

    Degrees of freedom = n - 1 = 21 - 1 = 20

    Based on the standard probability tables for t, the t score is:

    t = 0.860

    Substituting into equation 1:

    margin of error = 0.860 * 7.1 / sqrt (21)

    margin of error = 1.33

    The range is:

    range = 30.1 ± 1.33

    range = 28.77, 31.43

    Therefore the commute time to work is between 28.77 minutes and 31.43 minutes.
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