A new manufacturing method has been introduced to streamline the canning process of cherries. Although the time to fill a can has been reduced, the quality control manager is concerned about the uniformity of the amount of cherries in each can. The cans are labelled to contain 14.5 grams of cherries (the remaining volume consisting of natural juice). To be sure that this level has not been affected by the new canning method, the manager randomly samples 80 cans over an eight hour shift. The mean number of grams is 14.64. The population standard deviation is known to be 0.4g.
-The test statistic is _____.
A)3.13
B)1.98
C)3.96
D)-3.13
E)-1.98

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 population standard deviation, and $n$ is the sample size. Plugging in the given values: $z = \frac{14.64 - 14.5}{0.4/\sqrt{80}} = 3.13$.

A New Manufacturing Method Has Been Introduced to Streamline the Canning