Question

A states division of motor vehicles claims that 60% of teens pass their drivers test on the first attempt. an investigative reporter examines an srs of the dmv records for 125 teens, 86 of them passed the tests on their first try. Is there convincing evidence at the significance level that the DMV's claim is incorrect?

Answer 1

Answer: There is convincing evidence at the  the significance level that the DMV's claim is incorrect.

Step-by-step explanation:

Since we have given that

Hypothesis:

$H_0:p=0.6\\\\H_a:p\neq 0.6$

Probability of teens pass their drivers test on the first attempt = 60% = 0.60

Number of teens = 125

Number of them passed the tests on their first try = 86

$\hat{p}=\dfrac{86}{125}=0.688$

So, the value of test statistic would be

$z=\dfrac{\hat{p}-p}{\sqrt{\dfrac{p(1-p)}{n}}}\\\\z=\dfrac{0.688-0.60}{\sqrt{\dfrac{0.6\times 0.4}{125}}}\\\\z=\dfrac{0.088}{0.0438}\\\\z=2.009\\\\z\approx 2.01$

At α = 0.05% level of significance, critical value = 1.645

Since 1.645 < 2.01

So, we will reject the null hypothesis.

Hence, there is convincing evidence at the  the significance level that the DMV's claim is incorrect.