Find the P-value for the indicated hypothesis test. Round all proportions and standard scores to two decimal places.
-A random sample of 140 forty-year-old men contains 26% who smoke. Find the P-value for a test of the claim that the percentage of forty-year-old men that smoke is 22%.
A)0.1401
B)0.2542
C)0.2802
D)0.1271

Question

Quizplus · Accepted Answer

The P-value is found by first calculating the test statistic using the formula for a proportion z-test: $z = \frac{\hat{p} - p_0}{\sqrt{\frac{p_0(1-p_0)}{n}}}$, where $\hat{p}$ is the sample proportion, $p_0$ is the hypothesized population proportion, and $n$ is the sample size. Here, $\hat{p} = 0.26$, $p_0 = 0.22$, and $n = 140$. After calculating the z-score, you use a standard normal distribution table or a calculator to find the P-value corresponding to this z-score. The calculation results in a P-value around 0.2542, indicating the probability of observing a sample proportion at least as extreme as 26% if the true population proportion is 22%.

Find the P-Value for the Indicated Hypothesis Test