Question

Latoya wants to estimate the proportion of the seniors at her boarding school who like the cafeteria food. She interviews an SRS of $50$of the $175$ seniors and finds that $14$ think the cafeteria food is good.

Short answer

The $10\%$sample size condition does not meet.

Step-by-step solution

Step 1. Given information

$n=50$

The population is $175$seniors.

Step 2. Explanation

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

The sample should be less than $10\%$of the population. Here, $50$is more than $10\%$of the $175$. Hence, this condition does not meet.

The last condition is, $np=14\ge 10andn(1-p)=36\ge 10$which is met.