Find the P-value for the indicated hypothesis test. Round all proportions and standard scores to two decimal places.
-A medical school claims that more than 28% of its students plan to go into general practice. It is found that among a random sample of 130 of the school's students, 31% of them plan to go into general practice. Find the
P-value for a test of the school's claim.
A)0.2263
B)0.4472
C)0.2236
D)0.7764

Question

Quizplus · Accepted Answer

To find the P-value for the hypothesis test, we first calculate the test statistic using the formula for a proportion test statistic: $Z = \frac{\hat{p} - p_0}{\sqrt{\frac{p_0(1-p_0)}{n}}}$, where $\hat{p} = 0.31$, $p_0 = 0.28$, and $n = 130$. Plugging these values into the formula gives us a Z-score. Then, we find the P-value by looking up this Z-score in a standard normal distribution table or using a calculator. The P-value represents the probability of observing a sample proportion at least as extreme as the one observed (31% in this case), assuming the null hypothesis is true (that the true proportion is 28% or less). The correct P-value, rounded to four decimal places, is 0.2236, indicating the probability of observing a sample proportion of 0.31 or more, given the null hypothesis proportion is 0.28.

Find the P-Value for the Indicated Hypothesis Test