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Chapter 9: Q.49 (page 563)

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 α=0.05 significance level to help answer this question.

Short Answer

Expert verified

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

Step by step solution

01

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.

02

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,

H0:p=0.60H0:p≠0.60

using,

z=p^−p0p01−p0n=0.688-0.60.6(1-0.6)125=2.01

The p-value is

=2×P(Z>|z|)=0.446

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

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Most popular questions from this chapter

Two-sided test The one-sample t statistic from a sample of n=25observations for the two-sided test of H0:μ=64;Ha:μ≠64has the value t=-1.12.

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