Q.51 - The Practice of Statistics for AP

Question

(a) Construct and interpret a 95% confidence interval for the proportion of all teens in the state who passed their driving test on the first attempt.

(b) Explain what the interval in part (a) tells you about the DMV's claim.

Step-by-Step Solution

Answer

a. The confidence interval is$(0.607,0.769)$

b. It is an incorrect claim

Step 1: Introduction

A confidence interval is the mean of your estimate in addition to and minus the variation in that estimate. This is the scope of values you anticipate that your estimate should fall between if you re-try your test, within a certain degree of confidence. Confidence, in statistics, is one more method for describing probability.

Step 2: Explanation Part (a)

The number of teens is n =$125$

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

population proportion = $60\%=0.6$

$\stackrel{-}{p}=\frac{x}{n}=\frac{86}{125}=0.688$

Using,

$CI=\stackrel{-}{p}\pm z_{\alpha /2}\times \sqrt{\frac{\stackrel{-}{p}(1-\stackrel{-}{p})}{n}}$

 $CI=0.688\pm 1.960\times \sqrt{\frac{0.688(1-0.688)}{125}}$

$CI =(0.607,0.769)$ 

Step 3: Explanation Part (b)

We know that $0.60$ doesn't lie in the confidence interval. Hence,  It is an incorrect claim.