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Chapter 9: Q.109 (page 555)

Driver error can be listed as the cause of approximately 54% of all fatal auto accidents, according to the American Automobile Association. Thirty randomly selected fatal accidents are examined, and it is determined that 14 were caused by driver error. Using α = 0.05, is the AAA proportion accurate?

Short Answer

Expert verified

It appears that the American Automobile Association’s claim is accurate.

Step by step solution

01

State the null and alternate hypothesis. we have to conduct hypothesis test if all fatal auto accidents due to driver error take 54% of the driver according to American Automobile Association (AAA) or not, on average. 

H0:p=0.54;Ha:p≠0.54

02

Calculate the p-value using the normal distribution for proportions: 

p-value=0.4203

In one to two complete sentences, explain what the p-value means for this problem. If the null hypothesis is true (the proportion is 0.54), then there is a 0.4203 probability that the sample (estimated) proportion is 0.467 or more.

03

Compare α and the p-value:Indicate the correct decision (“reject” or “do not reject” the null hypothesis), the reason for it, and write an appropriate conclusion, using complete sentences.

alphadecisionreason for decision
0.05Do not reject the null hypothesis.
p-value>0.05

Conclusion: At the 5% significance level, there is not enough evidence to conclude that the proportion of fatal accidents that are the driver’s fault is not 0.54.

04

accuracy of the survey

It appears that the American Automobile Association’s claim is accurate.

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Most popular questions from this chapter

A Nissan Motor Corporation advertisement read, “The average man’s I.Q. is 107. The average brown trout’s I.Q.is4. So why can’t man catch brown trout?” Suppose you believe that the brown trout’s mean I.Q. is greater than four. You catch 12 brown trout. A fish psychologist determines the I.Q.s as follows: 5;4;7;3;6;4;5;3;6;3;8;5. Conduct a hypothesis test of your belief.

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The National Institute of Mental Health published an article stating that in any one-year period, approximately 9.5percent of American adults suffer from depression or a depressive illness. Suppose that in a survey of 100 people in a certain town, seven of them suffered from depression or a depressive illness. Conduct a hypothesis test to determine if the true proportion of people in that town suffering from depression or a depressive illness is lower than the percent in the general adult American population.

a. Is this a test of one mean or proportion?

b. State the null and alternative hypotheses.

H0:

Ha:

c. Is this a right-tailed, left-tailed, or two-tailed test?

d. What symbol represents the random variable for this test?

e. In words, define the random variable for this test.

f. Calculate the following:

i.x=

ii.role="math" localid="1649760873126" n=

iii.p'=

g. Calculate role="math" localid="1649760901479" σx=Show the formula set-up.

h. State the distribution to use for the hypothesis test.

i. Find the p-value.

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i. Decision:

ii. Reason for the decision:

iii. Conclusion (write out in a complete sentence):
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