Answer to Question #134055 in Statistics and Probability for Chanel

Question

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?

Answer 1

solution

maximum error $=2$

Standard deviation$=5.2$

Confidence level $=99\%$

Hence $\alpha = 1\%$

The Z-score $Z_{\alpha/2}=Z_{0.005}=2.58$

Sample size (n):

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

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

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