Test Hypotheses about a Population Mean with Known Using P-values
-Suppose you are using $\alpha = 0.01$ to test the claim that $\mu \leq 47$ using a P-value. You are given the sample statistics $\mathrm { n } = 40 , \overline { \mathrm { x } } = 48.8$, and $\sigma = 4.3$. Find the $\mathrm { P }$-value.
A) $0.0040$
B) $0.9960$
C) $0.0211$
D) $0.1030$

Question

Quizplus · Accepted Answer

The P-value is calculated using the Z-test formula for a known population standard deviation. The test statistic Z is calculated as $Z = \frac{\overline{x} - \mu}{\sigma / \sqrt{n}}$, where $\overline{x} = 48.8$, $\mu = 47$, $\sigma = 4.3$, and $n = 40$. Plugging in these values, we find $Z$, and then use the standard normal distribution to find the P-value corresponding to this Z-score. Given the claim is $\mu \leq 47$, we are looking at the upper tail, and the calculated P-value of 0.0040 indicates strong evidence against the null hypothesis in favor of the alternative hypothesis at the $\alpha = 0.01$ level.

Test Hypotheses About a Population Mean with Known Using P-Values α=0.01\alpha = 0.01α=0.01

Test Hypotheses About a Population Mean with Known Using P-Values $\alpha = 0.01$