Question

On a state driver's test, about $40\%$pass the test on the first try. We want to test if more than $40\%$pass on the first try. Fill in the correct symbol $(=,\ne ,\ge ,<,\le ,>)$for the null and alternative hypotheses.

a.${\mathrm{H}}_0:\mathrm{p}-0.40$

b.${\mathrm{H}}_{\mathrm{a}}:\mathrm{p}-0.40$

Short answer

a. Null hypotheses is less than or equal to$0.40$.

b. Alternative hypotheses is greater than$0.40$.

Step-by-step solution

Introduction

According to the null hypothesis, there is no difference between a proportion and the population's proportion.

The opposition of null hypotheses is stated by the alternative hypothesis

Explanation  (part a)  

On the first try not more than $40\%$is known as null hypotheses.

It is denoted by ${\mathrm{H}}_0$.

So,

${\mathrm{H}}_0:\mathrm{p}\le 0.40$

Explanation (part b)

On the first try more than $40\%$is known as alternative hypotheses.

It is denoted by ${\mathrm{H}}_{\mathrm{a}}$.

So,

${\mathrm{H}}_{\mathrm{a}}:\mathrm{p}>0.40$