Question

Home computers Jason reads a report that says $80\%$of U.S. high school

students have a computer at home. He believes the proportion is smaller than $0.80$at his large rural high school. Jason chooses an SRS of $60$students and finds that $41$have a computer at home. He would like to carry out a test at the $\alpha =0.05$significance level of $H_0:p=0.80$versus $H_a:p<0.80$, where $p$= the true

proportion of all students at Jason’s high school who have a computer at home. Check if the conditions for performing the significance test are met.

Short answer

Yes, the conditions are fulfilled.

Step-by-step solution

Given Information

It is given that
$\left(n\right)\text{is}60$

$\left(p\right)\text{is}0.80$

$H_0:p=0.80$

$H_a:p<0.80$

Checking the conditions

$p$refers to the proportion of students that own computer at home.

Conducting significance test, below conditions should be satisfied.

$n\times p\ge 10$

$n\times (1-p)\ge 10$

(1) $n\times p=60\times 0.8$

$=48>10$

(2) $n\times (1-p)=60\times (1-0.80)$

$=12>10$

Both conditions are satisfied.

So, we can conduct significance test.