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Statistics and Hypothesis Testing Practice Quiz

Question 1 (5 points)
A toy manufacturer produces battery-operated games. A random sample of 25 games averaged 15 operating hours on a set of batteries, with a standard deviation of 1.6 hours. Calculate the interval estimate with 95 percent confidence for the average operating time on a set of batteries for all of the manufacturer's games.

a. 14.11 - 15.9 hours
b. 14.18 - 15.82 hours
c. 14.34 - 15.66 hours
d. 14.37 - 15.63 hours

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Question 2 (10 points)

The Oklahoma Department of Public Safety believes that the average speed of automobiles traveling on I-35 is 65 mph. A random sample of 25 automobiles is taken between Norman and Moore. The sample has a mean speed of 72 mph and a standard deviation of 10 mph.

Test the department's belief that the average speed in I-35 is 65 mph.

a. Accept department's belief
b. Reject department's belief
c. Not enough information to make a judgment
d. Needs to undergo further testing

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Question 3 (10 points)
According to estimates made by the General Accounting Office (GAO), the Internal Revenue Service (IRS) answered 23.8 milliom telephone inquires during the 2001 tax season and 17% of the IRS offices provided answers that were wrong. How many IRS offices should be randonly selected and contacted in order to estimate the proportion of IRS offices that fail to correctly answer questions in 2002 about gift taxes? You want to be within 3 percent of the actual proportion with 95 percent confidence.

a. 602 offices
b. 1040 offices
c. 1068
d. 1844

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Question 4 (10 points)
A national sports magazine reports that the people who watch Monday night football are evenly divided between men and women. You conduct a random sample of those who regularly watch Monday night football. From a sample of 10,000 participants, 5,283 are men. Test the sport magazine's hypothesis that the proportion of men and women who watch Monday night football is evenly divided. Based on the results of your test the p-value is

a. 0.0000
b. 0.0911
c. 0.5000
d. 1.0000

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Question 5 (10 points)
A researcher wishes to determine if the majority of American adults over the age of 65 plan to vote Republican in the next presidential election. Let p represent the proportion of the population of all American adults over the age of 65 who plan to vote Republican in the next presidential election. An SRS of 1,844 adult American registered voters over the age of 65 indicates that 935 intent to vote Republican in the next presidential election. Perform a test of significance on the researchers premise. Based on the results of your test, the researcher's premise should be

a. rejected
b. not rejected.
c. considered undeterminable.
d. left for others to consider, because yu do not know the answer.

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Question 6 (5 points)

A newspaper conducted a statewide survey concerning the 2002 race for the state's senator. The newspaper took a stratified random sample of 1200 registered voters and found that 620 would vote for the Republican candidate.

Calculate a interval estimate with 99 percent confidence for the proportion of registered voters in the state that would vote for the Republican candidate.

a. LCL = 48%, UCL = 55.4%
b. LCL = 48.3%, UCL = 55.0%
c. LCL = 48.8%, UCL = 54.5%
d. Insufficient information to correct estimate the proportion.

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Question 7 (5 points)
Economic impact studies were performed to determine the effect of labor unions on wage rates. In the latest study, 10 union shops had an average wage rate of $22.07 with a standard deviation of $8.12. Twelve nonunion shops had an average wage of $24.17 with a standard deviation of $9.07. Calculate with 99 percent confidence an interval estimate for the difference in average wage rates between unionized and nonunionized shops.

a. $0 - $5.09
b. $0 - $5.63
c. $0 - $7.35
d. $0 - $8.34

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Question 8 (10 points)

While cable television companies in Minnesota are prohibited from holding exclusive rights to an area, the laws do not demand that a company face competition (Gross, 1993). Many subscribers feel that these de facto monopolies exploit consumers by charging excessive monthly cable fees. A congressional subcomittee is considering regulation of the cable industry. The subcomittee randomly sample basic cable rates for six companies that have no competition, and six companies with competitors. The observed rates are contained in the table below.

No Competition: $18.44 $26.88 $22.87 $25.78 $23.34 $27.52
Competition: $18.95 $23.74 $17.25 $20.14 $18.98 $20.14

Test to determine if there is a significant difference between the average basic cable rates of the two groups. (Hint: create two lists and input data.)

The p-value for this test is

a. 0.0000
b. 0.0146
c. 0.0291
d. 0.9709

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Question 9 (15 points)

While cable television companies in Minnesota are prohibited from holding exclusive rights to an area, the laws do not demand that a company face competition (Gross, 1993). Many subscribers feel that these de facto monopolies exploit consumers by charging excessive monthly cable fees. A congressional subcomittee is considering regulation of the cable industry. The subcomittee randomly sample basic cable rates for six companies that have no competition, and six companies with competitors. The observed rates are contained in the table below.

No Competition: $18.44 $26.88 $22.87 $25.78 $23.34 $27.52
Competition: $18.95 $23.74 $17.25 $20.14 $18.98 $20.14

Test to determine if there is a significant difference between the average basic cable rates of the two groups. (Hint: create two lists and input data.)

Based on the test, the congressional subcommittee should

a. reject the null hypothesis because there is a definite difference between the two average basic cable rates.
b. reject the subscribers claim because there is no significant difference between the two average basic cable rates.
c. pass the decision to the Federal Communications Commission (FCC) who would have direct regulatory control over the cable industry.
d. table the issue until after the next general election.

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Question 10 (5 points)

North Carolina State University looked at the factors that affect success of students in a required chemical engineering course. Students must get a C or better in the course to continue as chemical engineering majors. There were 65 students from urban/suburban backgrounds, and 52 of these students succeeded. Another 55 students were from rural or small-town backgrounds; 30 of these students succeeded in the course.

Calculate a 98 percent confidence interval for the difference in success rates between the two groups.

a. LCL = 9.1%, UCL = 41.8%
b. LCL = 6.0%, UCL = 44.9%
c. LCL = 4%, UCL = 47%
d. Cannot calculate

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Question 11 (15 points)

North Carolina State University looked at the factors that affect success of students in a required chemical engineering course. Students must get a C or better in the course to continue as chemical engineering majors. There were 65 students from urban/suburban backgrounds, and 52 of these students succeeded. Another 55 students were from rural or small-town backgrounds; 30 of these students succeeded in the course.

Test to see if there is a significance difference in the success rates of urban/surburban students and rural/small-town students. As a result of the test, one can concluded that:

a. that there is a significant difference in the success rates of the two groups.
b. that there is not a significant difference in the success rates of the two groups.
c. that there is insuficient information about the cultural and socioeconomic backgrounds of the students to support a comparison.
d. the two groups cannot be compared.

Solution Preview

This is a statistics practice quiz for a first semester statistics class. There are 11 problems on the quiz covering the following topics:

1. Confidence interval for a population mean
2. Hypothesis test for a ...

Solution Summary

This is a statistics practice quiz for a first semester statistics class. There are 11 problems on the quiz covering the following topics:

1. Confidence interval for a population mean
2. Hypothesis test for a population mean
3. Sample size for a population proportion (binomial proportion)
4. Hypothesis test for a population proportion
5. Confidence interval for a population proportion
6. Confidence interval for the difference between two population means
7. Hypothesis test for the difference between two population means
8. Confidence interval for the difference between two population proportions
9. Hypothesis test for the difference between two population proportions

I have provided the correct choice for each of the questions as well as details showing how the calculations for each question should be done.

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