The local pharmacy prides itself on the accuracy of the number of tablets that are dispensed in a 60 count prescription. The new manager feels that the pharmacy assistants might have become careless in counting due to an increase in the volume of prescriptions. To test this theory, the manager randomly selects 40 prescriptions requiring 60 tablets and recounts the number in each bottle. The manager finds a sample mean of 62.05 and a standard deviation of 4.45. Assume counts are approximately normally distributed.
-The test statistic is _____.
A)2.91
B)-2.91
C)-3.57
D)6.15
E)3.57

Question

Quizplus · Accepted Answer

To calculate the test statistic for the sample mean, use the formula $z = \frac{\bar{x} - \mu}{(\sigma/\sqrt{n})}$, where $\bar{x}$ is the sample mean, $\mu$ is the population mean (assumed to be 60 since that's the expected count), $\sigma$ is the standard deviation of the sample, and $n$ is the sample size. Plugging in the values: $z = \frac{62.05 - 60}{(4.45/\sqrt{40})}$ results in a z-score of approximately 2.91, indicating how many standard deviations the sample mean is from the population mean.

The Local Pharmacy Prides Itself on the Accuracy of the Number