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20 March, 12:33

The population standard deviation for the height of college football players is 2.7 inches. If we want to estimate a 95% confidence interval for the population mean height of these players with a 0.65 margin of error, how many randomly selected players must be surveyed? (Round up your answer to nearest whole number, do not include any decimals) Answer:

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  1. 20 March, 12:38
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    n = 66 (to the nearest whole number)

    66 randomly selected players must be surveyed

    Step-by-step explanation:

    Confidence interval can be defined as a range of values so defined that there is a specified probability that the value of a parameter lies within it.

    The confidence interval of a statistical data can be written as.

    x+/-zr/√n

    x+/-M. E

    M. E = zr/√n

    Making n the subject of formula;

    n = (zr/M. E) ^2 ... 1

    Given that;

    Mean = x

    Standard deviation r = 2.7 inches

    Number of samples = n

    Confidence interval = 95%

    z (at 95% confidence) = 1.96

    Margin of error M. E = 0.65 inches

    Substituting the given values into equation 1;

    n = (zr/M. E) ^2

    n = (1.96*2.7/0.65) ^2

    n = 66.28464852071

    n = 66 (to the nearest whole number)

    66 randomly selected players must be surveyed
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