CONFIDENCE INTERVAL FOR A POPULATION MEAN, m,

USING A T-SCORE

It is desired to estimate the mean percentage of body fat in male gymnasts on college teams. A random sample of 22 such athletes was selected and the percentage of body fat of each was recorded. These data are shown below.

Find a 99% confidence interval to estimate the mean percentage of body fat in male gymnasts on college teams.

 

SOLUTION

The parameter of interest is m, the mean percentage of body fat in male gymnasts on college teams. It is desired to find a 99% confidence interval for m.

 

COMMENTS ABOUT THE SOLUTION

  • This procedure is valid when the population of percentage of body fat of male gymnasts is normally distributed, and a random sample is selected from that population.
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  • The procedure  in this problem would also be valid if a large sample of percentages of body fat of male gymnasts was randomly selected even if the original distribution was not normal.  Generally speaking samples of 30 or more are considered large.
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  • Since the value of the sample standard deviation, s = 2.02, is known, and the value of the standard deviation of the population, s, is not known, the desired interval involved a t-score.
  • The usual structure for presenting the solution to a confidence interval was followed. All confidence interval solutions should follow this structure.
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  • If summary statistics were not provided, StatCrunch could be used to obtain the desired interval from the “raw data.” The calculated interval would be

    99% confidence interval results:
    μ : mean of Variable 

    Variable

    Sample Mean

    Std. Err.

    DF

    L. Limit

    U. Limit

    % Body Fat

    6.8772726

    0.4298863

    21

    5.66011

    8.094436

     

     

     The rest of the solution would be the same. First the same formula used to calculate the interval would be given; the calculations shown above would be done; and the same interpretation would be made.

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    The interval as calculated by StatCrunch is in blue. These values are slightly different than those given in the original solution due to the number of decimal places used by StatCrunch.

     

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