Q.28 - The Practice of Statistics for AP

Question

High tuition costs Glenn wonders what proportion of the students at his school think that tuition is too high. He interviews an SRS of $50$ of the $2400$ students at his college. Thirty-eight of those interviewed think tuition is too high.

Step-by-Step Solution

Answer

All three conditions for confidence interval is satisfied.

Step-1 Given Information

Given in the question that,

Population size$=2400$

number of sample$=50$

number of success$=38$ we have to calculate what proportion of the students at his school think that tuition is too high.

Step-2 Explanation

Three conditions must be met in order to construct a confidence interval. Random, Independent, and Normal are the conditions.

The requirement of randomness is met because the sample was drawn at random among the college students. The requirement for independence is satisfied because the sample size is less than 10% of the population size. In the study, there are $38$ success stories and $12$ failure stories. Because both the success and the success rate are more than ten. As a result, the typical condition is met. As a result, all three confidence interval conditions are met.