Question

Fire the coach!A college president says, “More than two-thirds of the alumni support my firing of Coach Boggs.” The president’s statement is based on $200$emails he has received from alumni in the past three months. The college’s athletic director wants to perform a test of $H_0:p=2/3$versus $H_a:p>2/3$, where $p$= the true proportion of the college’s alumni who favor firing the coach. Check if the conditions for performing the significance test are met.

Short answer

All conditions are fulfilled.

Step-by-step solution

Given Information

It is given that $n=200$

$p=\frac{2}{3}$

The null and alternate hypothesis are:

$H_0:p=\frac{2}{3}$

$H_a:p>\frac{2}{3}$

Calculation

The conditions important for significance test are:

• $n\times p\ge 10$: role="math" localid="1654611425980" $n\times p=200\times \frac{2}{3}=133.333>10$
  
• $n\times (1-p)\ge 10$: $n\times (1-p)=200\times \left(1-\frac{2}{3}\right)=66.667>10$

All condition are fulfilled, significance test can be performed.