Q.49 - The Practice of Statistics for AP

Question

A state's Division of Motor Vehicles (DMV) claims that 60 % of 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 this good evidence that the DMV's claim is incorrect? Carry out a test at the $\alpha =0.05$ significance level to help answer this question.

Step-by-Step Solution

Answer

There is good evidence that the DMV's claim is incorrect 

Step 1: Introduction

The significance level of an occasion (like a statistical test) is the probability that the occasion might have happened by some coincidence. If the level is quite low, that is to say, the probability of occurring by chance is tiny, we say the occasion is significant.

Step 2: Explanation

The number of teens is n = $125$

The number of teens that passed the test x= $86$

Population proportion = $60\%=0.6$

Calculating the null and alternative hypotheses,

$\begin{array}{r}{H}_0:p=0.60\\ H_0:p\ne 0.60\end{array}$

using,

$$\begin{gathered} z=\frac{\widehat{p}-p_0}{\sqrt{\frac{p_0\left(1-p_0\right)}{n}}}=\frac{0.688-0.6}{\sqrt{{\displaystyle \frac{0.6(1-0.6)}{125}}}} \\ =2.01 \end{gathered}$$

The p-value is

$=2\times P(Z>|z\left|\right)=0.446$

The p-value is less than the significance level hence there is good evidence that the DMV's claim is incorrect