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10 June, 16:19

The heights of a random sample of 50 college students showed a sample mean of 174.5 centimeters and a sample standard deviation of 6.9 centimeters. Construct a 98% confidence interval for the mean height of all college students.

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  1. 10 June, 18:14
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    Step-by-step explanation:

    We want to construct a 98% confidence interval for the mean height of all college students.

    Number of sample, n = 450

    Mean, u = 174.5 centimeters

    Standard deviation, s = 6.9 centimeters

    For a confidence level of 98%, the corresponding z value is 2.33. This is determined from the normal distribution table.

    We will apply the formula

    Confidence interval

    = mean ± z * standard deviation/√n

    It becomes

    174.5 ± 2.33 * 6.9/√450

    = 174.5 ± 2.33 * 0.325

    = 174.5 ± 0.757

    The lower end of the confidence interval is 174.5 - 0.757 = 173.743

    The upper end of the confidence interval is 174.5 + 0.757 = 175.257

    Therefore, with 98% confidence interval, the mean height of all college students is between 173.743 centimeters and 175.257 centimeters.
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