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9 August, 18:31

In a survey, the planning value for the population proportion is p * = 0.26. How large a sample should be taken to provide a 95% confidence interval with a margin of error of 0.05? (Round your answer up to nearest whole number.)

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  1. 9 August, 19:52
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    n = 296

    Sample size n = 296

    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.

    p+/-z√ (p (1-p) / n)

    x+/-M. E

    M. E = z√ (p (1-p) / n)

    Making n the subject of formula;

    n = (p (1-p) / (M. E/z) ^2) ... 1

    Given that;

    Proportion p = 0.26

    Number of samples n = ?

    Confidence interval = 95%

    z (at 95% confidence) = 1.96

    Substituting the values into equation 1;

    n = (0.26 (1-0.26)) / ((0.05/1.96) ^2)

    n = 295.649536

    n = 296

    Sample size n = 296
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