Question

Teen drivers A state’s Division of Motor Vehicles (DMV) claims that $60\%$

of all teens pass their driving test on the first attempt. An investigative reporter examines an SRS of the DMV records for $125$teens; $86$of them passed the test on their first try. Is there convincing evidence at the $\alpha =0.05$significance level that the DMV’s claim is incorrect?

Short answer

Sufficient evidence is present to show that at$5\%$significance level, DMC is incorrect.

Step-by-step solution

Given Information

It is given that

$\text{Hypothesized proportion}\left(p_0\right)=60\%=0.60$

$\left(n\right)=125,\left(\hat{p}\right)=\frac{x}{n}=\frac{86}{125}=0.688$

Explanation and Calculation

Null hypothesis: $H_0:p=0.60$

Alternate hypothesis: $H_a:p\ne 0.60$

Output from MINTAB is:

$P$value is less than $\alpha =0.05$, null hypothesis is rejected.

There is sufficient evidence to show that at$5\%$significance level, DMC is incorrect.