1. / In an instant lottery, your chances of winning are 0.2. If you play the lottery five times and outcomes are independent, the probability that you win at most once is
A) 0.7373. B) 0.4096. C) 0.0819. D) 0.2.
2. / The mean area  of the several thousand apartments in a new development by a certain builder is advertised to be 1250 square feet. A tenant group thinks this is inaccurate, because it is based on the square footage of apartments in an older development by the same builder. The group hires an engineer to measure a sample of apartments to verify its suspicion. The appropriate null and alternative hypotheses, H0 and Ha, for  are
A) / H0:  = 1250 and Ha:  < 1250.
B) / H0:  = 1250 and Ha:  > 1250.
C) / cannot be specified without knowing the size of the sample used by the engineer.
D) / H0:  = 1250 and Ha:  1250.
3. / Scores on the SAT Mathematics test (SAT-M) are believed to be normally distributed, with mean . The scores of a random sample of three students who recently took the exam are 550, 620, and 480. A 95% confidence interval for  based on these data is
A) 550.00 ± 128.58. B) 550.00 ± 173.88. C) 550.00 ± 105.01. D) 550.00 ± 142.00.
4. / A 99% confidence interval for the mean  of a population is computed from a random sample and found to be 6 ± 3. We may conclude
A) / there is a 99% probability that the true mean is 6, and there is a 99% chance that the true margin of error is 3.
B) / there is 1% probability that  is greater than 9.
C) / there is a 99% probability that  is between 3 and 9.
D) / if we took many, many additional random samples, and from each computed a 99% confidence interval for , approximately 99% of these intervals would contain .
5. / The time needed for college students to complete a certain paper and pencil maze follows a normal distribution with a mean of 70 seconds and a standard deviation of 15 seconds. You wish to see if the mean time  is changed by meditation, so you have a group of nine college students meditate for 30 minutes and then complete the maze. It takes them an average of = 64 seconds to complete the maze. Use this information to test the hypotheses
H0:  = 70, Ha:  70
at significance level  = 0.01. You conclude
A) / that H0 should not be rejected.
B) / this is a borderline case and no decision should be made.
C) / that H0 should be rejected.
D) / that Ha should be accepted.
6. / For which of the following counts would a binomial probability model be reasonable?
A) / the number of hearts in a hand of 5 cards dealt from a standard deck of 52 cards that has been thoroughly shuffled
B) / the number of sevens in a randomly selected set of five random digits from your table of random digits (Table B)
C) / the number of times you bought an instant lottery ticket last year.
D) / the number of phone calls received in a one-hour period
7. / Suppose I had measured the lifetimes of a random sample of 100 tires rather than 25. Which of the following statements is true?
A) / The margin of error for our 95% confidence interval would decrease.
B) /  would decrease.
C) / The margin of error for our 95% confidence interval would increase.
D) / The margin of error for our 95% confidence interval would stay the same, since the level of confidence has not changed.
8. / A level 0.90 confidence interval is
A) / an interval with margin of error ± 0.90, which is also correct 90% of the time.
B) / any interval with margin of error ± 0.90.
C) / an interval computed from sample data by a method guaranteeing that the probability the interval computed contains the parameter of interest is 0.90.
D) / an interval computed from sample data by a method that has probability 0.90 of producing an interval containing the true value of the parameter of interest.
9. / A company produces precision 1 meter (1000 mm) rulers. The actual distribution of lengths of the rulers produced by this company is normal, with mean  and standard deviation  = 0.02 mm. Suppose I select a simple random sample of four of the rulers produced by the company and I measure their lengths in mm. The results of these four measurements are
1,000.01999.981,000.001,000.01.
Based on these data, a 90% confidence interval for  is
A) 1,000.00 ± 0.0165. B) 1,000.00 ± 0.0196. C) 1,000.00 ± 0.0115. D) 1,000.00 ± 0.0082.
10. / A radio show runs a phone-in survey each morning. One morning in 2006, the show asked its listeners whether the United States should begin immediate withdrawal of troops from Iraq. The majority of those phoning in their responses answered “Yes, the United States should begin immediate withdrawal of troops from Iraq,” and the station reported the results as statistically significant. We may safely conclude
A) / it is unlikely that if all Americans were asked their opinion, that the result would differ from that obtained in the poll.
B) / very little other than the majority of those phoning in their responses believe the United States should begin immediate withdrawal of troops from Iraq.
C) / there is deep discontent in the nation with the war in Iraq.
D) / there is strong evidence that the majority of Americans believe the United States should begin immediate withdrawal of troops from Iraq.

Use the following to answer questions 11-13:

The superintendent of a large school district reads that 60% of middle school students have a personal site on myspace.com. She selects a sample of 50 middle school students at random from her district and has them complete a small survey. One of the questions asks if they have a personal site on myspace.com. Let X denote the number in the sample that say they have such a site.

11. / The probability that X is at least 35 is
A) about 0.3409. B) less than 0.0001. C) about 0.6591. D) about 0.0749.
12. / The mean of X is
A) 50. B) 60. C) 30. D) 20.
13. / The standard deviation of X is
A) 12. B) 3.46 C) 30. D) 5.48
14. / To assess the accuracy of a laboratory scale, a standard weight known to weigh 1 gram is repeatedly weighed a total of n times, and the mean of the weighings is computed. Suppose the scale readings are normally distributed, with unknown mean m and standard deviation  = 0.01 g. How large should n be, so that a 95% confidence interval for m has a margin of error of ± 0.0001?
A) 196 B) 38,416 C) 100 D) 10,000
15. / A university administrator obtains a sample of the academic records of past and present scholarship athletes at the university. The administrator reports that no significant difference was found in the mean GPA (grade point average) for male and female scholarship athletes (P = 0.287). This means
A) / the chance of obtaining a difference in GPAs between male and female scholarship athletes as large as that observed in the sample if there is no difference in mean GPAs is 0.287.
B) / the chance that a pair of randomly chosen male and female scholarship athletes would have a significant difference in GPAs is 0.287.
C) / the maximum difference in GPAs between male and female scholarship athletes is 0.287.
D) / the GPAs for male and female scholarship athletes are identical, except for 28.7% of the athletes.
16. / I collect a random sample of size n from a population and from the data collected compute a 95% confidence interval for the mean of the population. Which of the following would produce a new confidence interval with larger width (larger margin of error) based on these same data?
A) / Nothing can guarantee absolutely that you will get a larger interval. One can only say the chance of obtaining a larger interval is 0.05.
B) / Use a larger confidence level.
C) / Use a smaller confidence level.
D) / Use the same confidence level, but compute the interval n times. Approximately 5% of these intervals will be larger.

Answer Key

1. / A
2. / D
3. / B
4. / D
5. / A
6. / B
7. / A
8. / D
9. / A
10. / B
11. / D
12. / C
13. / B
14. / B
15. / A
16. / B

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