a. A simple random sample of size 80 has a mean of 7.31. The population standard deviation is 6.26. Construct a 99% confidence interval for

Question

a. A simple random sample of size 80 has a mean of 7.31. The population standard deviation is 6.26. Construct a 99% confidence interval for the population mean

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Thu Giang 5 years 2021-07-23T05:41:54+00:00 1 Answers 13 views 0

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  1. thuhuong
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    2021-07-23T05:42:59+00:00
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    Answer:

    5.503484≤x≤9.116516

    Step-by-step explanation:

    The formula for calculating the CI is expressed as;

    CI = x±z*s/√n

    x is the mean= 7.31

    z is the 99% z-score = 2.58

    s is the standard deviation = 6.26

    n is the sample size = 80

    Substitute into the formula

    CI = 7.31± 2.58*6.26/√80

    CI = 7.31± 2.58*6.26/8.94

    CI = 7.31± (2.58*0.7002)

    CI = 7.31±1.806516

    CI = (7.31-1.806516, 7.31+1.806516)

    CI = (5.503484, 9.116516)

    Hence the 99% confidence interval for the population mean is

    5.503484≤x≤9.116516

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