Q.27 - The Practice of Statistics for AP

Question

Rating dorm food Latoya wants to estimate what proportion of the seniors at her high school like the cafeteria food. She interviews an SRS of $50$ of the $175$ seniors living in the dormitory. She finds that $14$ think the cafeteria food is good.

Step-by-Step Solution

Answer

All three conditions for confidence interval is not satisfied

Step-1 Given Information

Given in the question that,

Sample size $=50$

Total number of seniors$=175$

number of success$=14$ we have to check whether each of the conditions is met for calculating a confidence interval for the population proportion $p$.

Step-2 Explanation

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

Since Latoya interviewed seniors staying in the dormitory at random, the condition of randomness has been satisfied. The sample size is greater than $10\%$ of the total number of seniors in the hostel. As a result, the $10\%$ criterion is not met. As a result, the criteria for independence is not met. The survey's success rate is $14$ percent, which is higher than the national average of $10$ percent. As a result, the typical condition is met. As a result, none of the three confidence interval conditions are met.