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15 October, 21:42

It is desired to estimate the mean gpa of each undergraduate class at a large university. assume that the variance of the gpas is 1.44. how large a sample is necessary to estimate the mean gpa within 0.25 at the 99% confidence level

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  1. 15 October, 22:38
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    First let us define the variables in this problem:

    variance, s^2 = 1.44 - - - >taking the square root gives standard deviation, s = 1.2

    margin of error, MOE = 0.25

    confidence level = 0.99

    N = number of students required

    Using the standard distribution table for z, p = 0.99 occurs when z = 2.58

    The formula for Margin of Error is given as:

    MOE = z * s / sqrt N

    0.25 = 2.58 * 1.2 / sqrt N

    sqrt N = 12.384

    N = 153.36 = 154

    Therefore the sample should be at least 154 students to estimate the mean gpa within 0.25.
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