Question

A police officer claims that the proportion of drivers wearing seat belts is more than 55%. To test this claim, a random sample of drivers are checked for seat belt usage. Assume that the test statistic for this hypothesis test is 1.87. Assume the critical value for this hypothesis test is 1.645. Come to a decision for the hypothesis test and interpret your results with respect to the original claim.

Select the correct answer below:

a. Fail to reject the null hypothesis There is not enough evidence to support the claim that the proportion of drivers wearing seat belts is more than 55%.
b. Reject the null hypothesis There is enough evidence to support the claim that the proportion of drivers wearing seat belts is more than 55%.

Answer 1

Option B)

Reject the null hypothesis There is enough evidence to support the claim that the proportion of drivers wearing seat belts is more than 55%.

Explanation:

We are given the following in the question:

p = 55% = 0.55

First, we design the null and the alternate hypothesis

`H_(0): p = 0.55\\H_A: p > 0.55`

The null hypothesis sates that 55% of of drivers wear seat belts and the alternate hypothesis states that there is a increase in proportion of drivers wearing seat belts.

This is a one-tailed(right) test.

Formula:

`z = \frac{\hat{p}-p}{\sqrt{(p(1-p))/(n)}}`

Putting the values, we get,

`z = 1.87`

Now,
`z_(critical) = 1.645`

Since,

`z_(stat) > z_(critical)`

We fail to accept the null hypothesis and reject it. We accept the alternate hypothesis.

Conclusion:

There is enough evidence to support the claim that that the proportion of drivers wearing seat belts is more than 55%.

Option B)

Reject the null hypothesis There is enough evidence to support the claim that the proportion of drivers wearing seat belts is more than 55%.