Question

In 2008, the population of part-time college students was 60% female. We are curious if the proportion has decreased this year. We test the hypotheses: Ho: p=0.60p = 0.60 and Ha<0.60p, where p is the proportion of part-time college students that are female this year. Which of the following p-hat values will give the smallest p-value? a. 0.58 b.0.48 c.0.40

Answer 1

Solution:
Given:

the hypotheses are:

Ho: p=0.60 and Ha: p <0.60

If sample proportion p-hat ( ) is close to population proportion p, then difference between them would be smaller and hence results in larger p-value.

If sample proportion p-hat ( ) is more away from population proportion p, hen difference between them would be larger and hence result in smaller p-value, because if difference is large, then obtained test statistic value would be close to tails of the distribution instead of center of the distribution and hence area below test statistic value is the p-value which would be small when test statistic value is close to tails of the distribution.

Thus correct answer is:

c) 0.40