Test Hypotheses about a Population Mean with Known Using P-values
-Suppose you are using $\alpha = 0.05$ to test the claim that $\mu \neq 25$ using a P-value. You are given the sample statistics $\mathrm { n } = 35 , \overline { \mathrm { x } } = 24.1$, and $\sigma = 2.7$. Find the $\mathrm { P }$-value.
A) $0.0448$
B) $0.0591$
C) $0.1003$
D) $0.0244$

Question

Quizplus · Accepted Answer

To find the P-value for testing the claim that $\mu \neq 25$, we first calculate the test statistic using the formula $z = \frac{\overline{x} - \mu}{\sigma / \sqrt{n}}$, where $\overline{x} = 24.1$, $\mu = 25$, $\sigma = 2.7$, and $n = 35$. Plugging in the values, we get $z = \frac{24.1 - 25}{2.7 / \sqrt{35}}$. This yields a z-value, which we then use to find the two-tailed P-value from the standard normal distribution. The closest P-value among the options given is 0.0448, indicating that the result is statistically significant at the $\alpha = 0.05$ level for a two-tailed test.

Test Hypotheses About a Population Mean with Known Using P-Values α=0.05\alpha = 0.05α=0.05

Test Hypotheses About a Population Mean with Known Using P-Values $\alpha = 0.05$