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30 January, 22:41

What is the approximate width of a 90 percent confidence interval for the true population proportion if there are 12 successes in a sample of 25?

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  1. 31 January, 00:15
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    To find for the value of the approximate width or margin of error, we make use of the following formula:

    approximate width = ± z [p (1 - p) / n]^0.5

    where,

    z = z score can be obtained using normal distribution tables at 90% confidence level

    p = probability of success

    n = number of samples = 25

    Using the standard distribution tables, the value of z at 90% level is:

    z = 1.645

    The probability of success is 12 out of 25, therefore:

    p = 12 / 25 = 0.48

    Therefore the approximate width is:

    approximate width = ± 1.645 [0.48 (1 - 0.48) / 25]^0.5

    approximate width = ± 1.645 (0.0999)

    approximate width = ± 0.164
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