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13 December, 16:28

Construct a 95 % confidence interval to estimate the population mean using the data below. x overbarequals37 sigmaequals10 nequals44 With 95 % confidence, when nequals44 the population mean is between a lower limit of 52.82 and an upper limit of 58.21. (Round to two decimal places as needed.)

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  1. 13 December, 16:38
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    With 95% confidence when n equals 44, the population mean is between a lower limit of 33.96 and an upper limit of 40.04

    Step-by-step explanation:

    Confidence Interval = mean + or - Error margin (E)

    mean = 37

    sd = 10

    n = 44

    degree of freedom = n - 1 = 44 - 1 = 43

    t-value corresponding to 43 degrees of freedom and 95% confidence level is 2.0165

    E = t * sd/√n = 2.0165*10/√44 = 3.04

    Lower limit = mean - E = 37 - 3.04 = 33.96

    Upper limit = mean + E = 37 + 3.04 = 40.04

    95% confidence interval is between 33.96 and 40.04
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