Alyson Silvastein, a scientist, reports that the average number of hours a person can go
without sleep and still function normally is 29 with a standard deviation of five hours. A
sample of 49 people had an average of 31 hours that they could go without sleep and still
function normally. The test value for this hypothesis would be 2.8.

Question

Quizplus · Accepted Answer

The correct test value (z-score) 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 ($\bar{x} = 31$, $\mu = 29$, $\sigma = 5$, $n = 49$), we get $z = \frac{31 - 29}{(5 / \sqrt{49})} = \frac{2}{(5 / 7)} = \frac{2}{5/7} = 2 \times \frac{7}{5} = 2.8$. My explanation was incorrect; the calculation provided in the statement actually leads to the correct test value of 2.8, based on the formula and values given.

Alyson Silvastein, a Scientist, Reports That the Average Number of Hours