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26 May, 15:55

In a random sample of 19 people, the mean commute time to work was 30.7 minutes and the standard deviation was 7.3 minutes. Assume the population is normally distributed and use a t-distribution to construct a 99 % confidence interval for the population mean mu. What is the margin of error of mu ? Interpret the results.

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  1. 26 May, 17:38
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    The margin of error of mu is 4.82 minutes

    99% confidence interval for mu is between a lower limit of 25.88 minutes and an upper limit of 35.52 minutes

    Step-by-step explanation:

    Margin of error (E) = t * sd/√n

    population mean (mu) = 30.7 minutes

    sd = 7.3 minutes

    n = 19

    degree of freedom = n - 1 = 19 - 1 = 18

    confidence level = 99%

    t-value corresponding to 18 degrees of freedom and 99% confidence level is 2.878

    E = 2.878 * 7.3/√19 = 4.82 minutes

    Lower limit = mu - E = 30.7 - 4.82 = 25.88 minutes

    Upper limit = mu + E = 30.7 + 4.82 = 35.52 minutes

    99% confidence interval for the mean commute time to work is between 25.88 and 35.52 minutes.
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