A wine manufacturer is concerned that the percentage of alcohol in each bottle may not be the 13% as advertised on the bottle. A random sample of 31 bottles is tested. The average alcohol percentage is 12.58% and the standard deviation is 0.25%. Assume alcohol content is normally distributed.
-The test statistic to test these hypotheses is _____.
A)9.35
B)-9.35
C)4.68
D)-4.68
E)-1.68

Question

Quizplus · Accepted Answer

The test statistic is calculated using the formula: $z = \frac{\bar{x} - \mu}{(\sigma/\sqrt{n})}$, where $\bar{x}$ is the sample mean, $\mu$ is the population mean, $\sigma$ is the standard deviation, and $n$ is the sample size. Plugging in the given values: $z = \frac{12.58 - 13}{(0.25/\sqrt{31})}$ gives $z = -9.35$.

A Wine Manufacturer Is Concerned That the Percentage of Alcohol