Answer to Question #134055 in Statistics and Probability for Chanel

Question #134055
Ramos is concerned about the number of prescriptions his elderly clients have. He would like to create a 99% confidence interval for the mean number of prescriptions per client with a maximum error of 2 prescriptions. Assuming a standard deviation of 5.2 prescriptions, what is the minimum number of clients he must sample?
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Expert's answer
2020-09-21T15:44:33-0400

solution


maximum error =2=2

Standard deviation=5.2=5.2


Confidence level =99%=99\%

Hence α=1%\alpha = 1\%

The Z-score Zα/2=Z0.005=2.58Z_{\alpha/2}=Z_{0.005}=2.58


Sample size (n):



n=(Zα/2Standard DeviationMaximum Error)2n = (\frac{Z_{\alpha/2}* Standard\ Deviation}{Maximum\ Error})^2

=(2.585.22)2=44.997= (\frac{2.58*5.2}{2})^2=44.997

answer: the minimum number of clients required for the test is 45

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