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    Suppose a sample of 50 is taken from a population with a standard deviation of 27 and that the sample mean is 86. Establish a 95.5% interval estimate for the population mean. Suppose, instead, that the sample size was 5000. Establish a 95.5% interval estimate for the population mean. Why might you prefer one estimate over the other?

    © BrainMass Inc. brainmass.com December 24, 2021, 7:23 pm ad1c9bdddf
    https://brainmass.com/statistics/confidence-interval/computing-confidence-interval-mean-184969

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    Sampling
    Suppose a sample of 50 is taken from a population with a standard deviation of 27 and that the sample mean is 86. Establish a 95.5% interval estimate for the population mean, Suppose, instead, that the sample size was 5000. Establish a 95.5% interval estimate for the population mean. Why might you prefer one estimate over the other?
    Answer
    The confidence interval is given by
    Sample Size 50
    Confidence Interval Estimate for the Mean

    Data
    Sample Standard Deviation 27
    Sample Mean 86
    Sample Size 50
    Confidence Level 95.5%

    Intermediate Calculations
    Standard Error of the Mean 3.818376618
    Degrees of Freedom 49
    t Value 2.057296743
    Interval Half Width 7.855533781

    Confidence Interval
    Interval Lower Limit 78.14
    Interval Upper Limit 93.86
    Sample Size 5000
    Confidence Interval Estimate for the Mean

    Data
    Sample Standard Deviation 27
    Sample Mean 86
    Sample Size 5000
    Confidence Level 95.5%

    Intermediate Calculations
    Standard Error of the Mean 0.381837662
    Degrees of Freedom 4999
    t Value 2.005157632
    Interval Half Width 0.765644702

    Confidence Interval
    Interval Lower Limit 85.23
    Interval Upper Limit 86.77
    Thus the confidence interval is narrow when the sample size is large. Thus the second interval is preferable.

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    © BrainMass Inc. brainmass.com December 24, 2021, 7:23 pm ad1c9bdddf>
    https://brainmass.com/statistics/confidence-interval/computing-confidence-interval-mean-184969

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