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Hypothesis Testing for Police Road Blocks

Please see the attached file.

Consider the use of Police road blocks to detect people that are driving intoxicated.

a. What are the null and alternative hypothesis?

b. What are the type I and type II errors in this case?

c. Which type of error is more costly?

d. Based on your answer to part (c), what value of α would you recommend for this test?

e. If the number of Police road blocks were to be increased, how would the probabilities of type I and type II errors be affected?

f. If α is to be increased, should the number of Police road blocks be increased or decreased?

Problem 7-53

The sales of home appliances have increased greatly in recent years. A study sponsored by the home appliance industry is aimed at testing the hypothesis that 6% of all consumers purchased new appliances during the June-September period. Industry analysts have no prior suspicion as to whether the proportion of consumers who bought new appliances during the period in question is higher or lower than stated and merely want to check the claim. A random sample of 2,000 consumers nationwide shows that 142 bought new appliances during the period. Is this a one-tailed or a two-tailed test? What is the p-value? State your conclusion.

Problem 7-56

A graduate student comes out of college with an average debt of $25,000. A sample of 200 graduate students showed that they had an average debt of $30,000 with a standard deviation of $10,000. State the null and alternative hypotheses and carry out the test at the 5% level of significance.

Problem 7-70

Environmental changes have recently been shown to improve firms' competitive advantages. The approach is called the multiple-scenario approach. A study was designed to find the percentage of the Fortune top 1,000 firms that use the multiple-scenario approach. The null hopothesis was that 30% or fewer of the firms use the approach. A random sample of 166 firms in the Fortune top 1,000 was chosen, and 59 of the firms replied that they used the multiple-scenario approach. Conduct the hypothesis test at α = 0.05. What is the p-value? (Do you need to use the finite-population correction factor?)

Problem 7-73

Microsoft Corporation makes software packages for use in microcomputers. The company believes that if at least 25% of present owners of microcomputers of certain types would be interested in a particular new software package, then the company will make a profit if it markets the new package. A company analyst therefore wants to test the null hypothesis that the proportion of owners of microcomputers of the given kinds who will be interested in the new package is at most 0.25, versus the alternative that the proportion is greater than 0.25.. A random sample of 300 microcomputer owners shows that 94 are interested in the new Microsoft package. Should the company market its new product? Report the p-value.

Solution Preview

Please see the attached file.

Chapter 7 Hypothesis testing: Problem 7-9

Consider the use of Police road blocks to detect people that are driving intoxicated.
a. What are the null and alternative hypotheses?
H0: There is no difference in the number of people driving intoxicated and without intoxication after the police blocks are introduced.
HA: There is a difference in the number of people driving intoxicated and without intoxication after the police blocks are introduced.

b. What are the type I and type II errors in this case?
Type I error is the error of rejecting a null hypothesis when it is true. Therefore, Type I error in this case would be committed if it is concluded that there is a difference in the number of people driving intoxicated and without intoxication after the police blocks are introduced, when it is not.

Type II error is the error of failing to reject the alternative is true. Therefore, Type II error in this case would be committed if it is concluded that there is no difference in the number of people driving intoxicated and without intoxication after the police blocks are introduced, when there indeed is a difference.

c. Which type of error is more costly?
Type I error is more costly.

d. Based on your answer to part (c), what value of α would you recommend for this test?
 = 5%

e. If the number of Police road blocks were to be increased, how would the probabilities of type I and type II errors be affected?
The probability of Type I error would remain the same, but that for TYpe II error would increase.

f. If α is to be increased, should the number of Police road blocks be increased or ...

Solution Summary

The solution carries out hypothesis testing to determine if Police road blocks can detect people that are driving intoxicated.

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