Suppose you are testing the null hypothesis that a population mean is less than or equal to 46, against the alternative hypothesis that the population mean is greater than 46.The sample size is 25 and α =.05.If the sample mean is 50 and the population standard deviation is 8, the observed z value is _______.
A)2.5
B)-2.5
C)6.25
D)-6.25
E)12.5

Question

Quizplus · Accepted Answer

The observed z value 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 under the null hypothesis, $\sigma$ is the population standard deviation, and $n$ is the sample size. Plugging in the given values: $z = \frac{50 - 46}{8/\sqrt{25}} = \frac{4}{8/5} = \frac{4}{1.6} = 2.5$.

Suppose You Are Testing the Null Hypothesis That a Population