A study seeks to determine whether the proportion of Dutch boys who listen to music at high volume is greater than this proportion for Dutch girls. After checking to make sure that all of the necessary conditions were met, we calculated the value of the z test statistic to be z = 2.999. Which of the following is the P-value associated with this test?
A)0
B)0.0014
C)0.0028
D)0.9986
E)0.9972

Question

A study seeks to determine whether the proportion of Dutch boys who listen to music at high volume is greater than this proportion for Dutch girls. After checking to make sure that all of the necessary conditions were met, we calculated the value of the z test statistic to be z = 2.999. Which of the following is the P-value associated with this test? ​
A)0
B)0.0014
C)0.0028
D)0.9986
E)0.9972

Quizplus · Accepted Answer

The P-value is the probability of observing a test statistic as extreme as, or more extreme than, the observed value under the null hypothesis. Since this is a one-tailed test (we're looking for whether one proportion is greater than the other), we find the area to the right of z = 2.999 in the standard normal distribution. Using a Z-table or calculator, the area to the left of z = 2.999 is approximately 0.9986, so the area to the right (our P-value) is 1 - 0.9986 = 0.0014.

A Study Seeks to Determine Whether the Proportion of Dutch