# To test the null hypothesis that the difference between two population proportions equals some constant (delta_{0}), not

## Question:

To test the null hypothesis that the difference between two population proportions equals some constant \(\delta_{0}\), not necessarily 0 , we can use the statistic

which, for large samples, is a random variable having the standard normal distribution.

**(a)** With reference to Exercise 10.32, use this statistic to test at the 0.05 level of significance whether the true proportion of units requiring rework is now at least \(4 \%\) less than before the improvements were made.

**(b)** In a true-false test, a test item is considered to be good if it discriminates between well-prepared students and poorly prepared students. If 205 of 250 well-prepared students and 137 of 250 poorly prepared students answer a certain item correctly, test at the 0.01 level of significance whether for the given item the proportion of correct answers can be expected to be at least \(15 \%\) higher among well-prepared students than among poorly prepared students.

Data From Exercise 10.32

## Step by Step Answer:

**Related Book For**

## Probability And Statistics For Engineers

**ISBN:** 9780134435688

9th Global Edition

**Authors:** Richard Johnson, Irwin Miller, John Freund