Question

Walking to school A recent report claimed that $13\%$of students typically walk to school. DeAnna thinks that the proportion is higher than $0.13$at her large elementary school. She surveys a random sample of $100$students and finds that $17$typically walk to school. DeAnna would like to carry out a test at the $\alpha =0.05$significance level of $H_0:p=0.13$versus $H_a:p>0.13$, where $p$= the true proportion of all students at her elementary school who typically walk to school. Check if the conditions for performing the significance test are met.

Short answer

The conditions are fulfilled.

Step-by-step solution

Given Information

It is given that $n=100$

$p=0.13$

The null and alternate hypothesis are

$H_0:p=0.13$

$H_a:p>0.13$

$p$ proportion of students that walk to schools.

Checking conditions for significance test

The conditions to be fulfilled are:

(a) $n\times p\ge 10$: $n\times p=100\times 0.13=13>10$

(b) $n\times (1-p)\ge 10$: $n\times (1-p)=100\times (1-0.13)=870>10$

Since both conditions re fulfilled, significance test can be performed.