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18 January, 15:35

A medical researcher wants to investigate the amount of time it takes for patients' headache pain to be relieved after taking a new prescription painkiller. she plans to use statistical methods to estimate the mean of the population of relief times. she believes that the population is normally distributed with a standard deviation of 15 minutes. how large a sample should she take to make an estimate within 3 minutes of the mean time with 96% confidence?

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  1. 18 January, 15:37
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    We calculate the z-score, by evaluating the z value of 0.96/2 = 0.48

    The z-score for 0.48 = 2.054

    Next, we multiply the z-score by the standard deviation.

    i. e. 2.054 x 15 = 30.81

    Next, we divide by the margin of error. (from the question, we want to estimate to within 3 minutes of the mean, thus our margin of error is 3.)

    i. e. 30.81 / 3 = 10.27

    Finally, we square the outcome,

    i. e. 10.27^2 = 105.47

    Therefore, to estimate within 3 minutes of the mean with 96% confidence, the researcher should take a minimum of 106 samples.
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