Chapter 8.2, Problem 30E

To determine

To explain whether the conditions for calculating a confidence interval for the population proportion.

Answer to Problem 30E

All the conditions met.

Explanation of Solution

Given:

  $n=50$

The population is 2400 students

The condition of random selection is satisfied because they selected an SRS of students.

The sample should be less than 10% of the population. Here, 50 is less than 10% of the 2400. Hence, this condition met.

The last condition is, number of success and failure must be $\ge 10$ . Therefore, number of successes =38 and number failures = 50-38 $\ge 10$ which is met. Hence, all the conditions of confidence interval are met.