Test Hypotheses about a Population Mean with Known Using P-values
-Suppose you are using $\alpha = 0.05$ to test the claim that $\mu 24$ using a P-value. You are given the sample statistics $n = 50 , \bar { x } = 24.3$, and $\sigma = 1.2$. Find the P-value.
A) $0.0384$
B) $0.1321$
C) $0.0128$
D) $0.0012$

Question

Test Hypotheses about a Population Mean with Known Using P-values
-Suppose you are using $\alpha = 0.05$ to test the claim that $\mu > 24$ using a P-value. You are given the sample statistics $n = 50 , \bar { x } = 24.3$, and $\sigma = 1.2$. Find the P-value.
A) $0.0384$
B) $0.1321$
C) $0.0128$
D) $0.0012$

Quizplus · Accepted Answer

To find the P-value, we first calculate the test statistic using the formula $Z = \frac{\bar{x} - \mu}{\sigma/\sqrt{n}}$, where $\bar{x} = 24.3$, $\mu = 24$, $\sigma = 1.2$, and $n = 50$. Plugging in the values, we get $Z = \frac{24.3 - 24}{1.2/\sqrt{50}}$, which gives a Z-score. Then, we use the Z-score to find the P-value from the standard normal distribution table or a calculator, which corresponds to the probability of observing a test statistic as extreme as, or more extreme than, the one calculated, given that the null hypothesis is true. The correct P-value for this scenario, based on the calculation, is $0.0384$, indicating the probability of observing a sample mean of 24.3 or more extreme, assuming the population mean is 24.

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 $\alpha = 0.05$