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Chapter 9: Q 51. (page 583)

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 125teens; 86of them passed the test on their first try. Is there convincing evidence at the α=0.05significance level that the DMV’s claim is incorrect?

Short Answer

Expert verified

Sufficient evidence is present to show that at5%significance level, DMC is incorrect.

Step by step solution

01

Given Information

It is given that

Hypothesized proportionp0=60%=0.60

(n)=125,(p^)=xn=86125=0.688

02

Explanation and Calculation

Null hypothesis: H0:p=0.60

Alternate hypothesis: Ha:p≠0.60

Output from MINTAB is:

Pvalue is less than α=0.05, null hypothesis is rejected.

There is sufficient evidence to show that at5%significance level, DMC is incorrect.

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Most popular questions from this chapter

Significance tests A test of H0:p=0.65 against Ha:p<0.65

based on a sample of size 400 yields the standardized test statistic z=−1.78 .

a. Find and interpret the P-value.

b. What conclusion would you make at the α=0.10 significance level? Would

your conclusion change if you used α=0.05 instead? Explain your reasoning.

c. Determine the value of p⏜= the sample proportion of successes.

Bullies in middle school A media report claims that more than 75%of

middle school students engage in bullying behavior. A University of Illinois study on aggressive behavior surveyed a random sample of 558middle school students. When asked to describe their behavior in the last 30days, 445students admitted that they had engaged in physical aggression, social ridicule, teasing, name-calling, and issuing threats —all of which would be classified as bullying. Do these data provide convincing evidence at the α=0.05significance level that the media report’s claim is correct?

Bags of a certain brand of tortilla chips claim to have a net weight of 14ounces. Net weights vary slightly from bag to bag and are Normally distributed with mean μ . A representative of a consumer advocacy group wishes to see if there is convincing evidence that the mean net weight is less than advertised and so intends to test the hypotheses

H0:μ=14Ha:μ<14

A Type I error in this situation would mean concluding that the bags

a. are being underfilled when they aren’t.

b. are being underfilled when they are.

c. are not being underfilled when they are.

d. are not being underfilled when they aren’t.

e. are being overfilled when they are underfilled

A95%confidence interval for the proportion of viewers of a certain reality television

show who are over 30 years old is (0.26,0.35). Suppose the show's producers want to est the hypothesis \H0:p=0.25against Ha: Ha:p≠0.25. Which of the following is an appropriate conclusion for them to draw at the α=0.05

a. Fail to reject H0; there is convincing evidence that the true proportion of viewers of this reality TV show who are over 30 years old equals 0.25

b. Fail to reject H0there is not convincing evidence that the true proportion of viewers of this reality TV show who are over 30 years old differs from0.25.

c. Reject H0; there is not convincing evidence that the true proportion of viewers of this reality TV show who are over 30 years old differs from 0.25

. d. Reject H0; there is convincing evidence that the true proportion of viewers of this reality TV show who are over 30 years old is greater than 0.25.

e. Reject H0; there is convincing evidence that the true proportion of viewers of this reality TV show who are over 30 years old differs from0.25.

Significance tests A test of Ho:p=0.5versus Ha:p>0.5based on

a sample of size 200yields the standardized test statistic z=2.19. Assume that the conditions for performing inference are met.

a. Find and interpret the P-value.

b. What conclusion would you make at the α=0.01 significance level? Would

your conclusion change if you used α=0.05 instead? Explain your reasoning.

c. Determine the value of p^= the sample proportion of successes.
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