Question

Mr. Tabor believes that less than $75\%$ of the students at his school completed their math homework last night. The math teachers inspect the homework assignments from a random sample of $50$ students at the school.

Short answer

$$\begin{gathered} H_0:p=75\%=0.75 \\ {H}_a:p<0.75 \end{gathered}$$

Step-by-step solution

Step 1. Given information

Claim is proportion is less than$75\%$.

Step 2. Explanation

The null hypothesis statement is that the population is equal to the value mentioned in the claim:

$H_0:p=75\%=0.75$

The claim is either the null hypothesis or the alternative hypothesis. The null hypothesis statement is that the population proportion is equal to the value given in the claim. If the null hypothesis is the claim, then the alternative hypothesis statement is the opposite of the null hypothesis.

$H_a:p<0.75$