Download 1. USA Today reported that speed skater Bonnie Blair had "won the

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MULTIPLE CHOICE
1. USA Today reported that speed skater Bonnie Blair had "won the USA’s heart, " according to a USA
Today/CNN/Gallup poll conducted on the final Thursday of the 1994 Winter Olympics. When asked who the hero of
the Olympics was, 65 percent of the respondents chose Blair, who won five gold medals. The poll of 615 adults, done
by telephone, had a margin of error of 4 percent. Which of the following statements best describes what is meant by
the 4 percent margin of error?
A) About 4 percent of adults were expected to change their minds between the time of the poll and its publication in
USA Today.
B) About 4 percent of adults did not have telephones.
C) About 4 percent of the 615 adults polled refused to answer.
D) Not all of the 615 adults knew anything about the Olympics.
E) The difference between the sample percentage and the population percentage is likely to be less than 4 percent.
2. A random sample of the costs of repair jobs at a large muffler repair shop produces a mean of $127.95 and a standard
deviation of $24.03. If the size of this sample is 40, which of the following is an approximate 90 percent confidence
interval for the average cost of a repair at this repair shop?
A) $127.95 ± $4.87
B) $127.95 ± $6.25
C) $127.95 ± $7.45
D) $127.95 ± $30.81
E) $127.95 ± $39.53
3. A 95 percent confidence interval of the form p̂ ± E will be used to obtain an estimate for an unknown population
proportion p. If p̂ is the sample proportion and E is the margin of error, which of the following is the smallest sample
size that will guarantee a margin of error of at most 0.08?
A) 25
B) 100
C) 175
D) 250
E) 625
4. A survey was conducted to determine what percentage of college seniors would have chosen to attend a different
college if they had known then what they know now. In a random sample of 100 seniors, 34 percent indicated that
they would have attended a different college. A 90 percent confidence interval for the percentage of all seniors who
would have attended a different college is
A) 24.7% to 43.3%
B) 25.8% to 42.2%
C) 26.2% to 41.8%
D) 30.6% to 37.4%
E) 31.2% to 36.8%
5. A test engineer wants to estimate the mean gas mileage ~ (in miles per gallon) for a particular model of automobile.
Eleven of these cars are subjected to a road test, and the gas mileage is computed for each car.
A dotplot of the 11 gas-mileage values is roughly symmetrical and has no outliers. The mean and standard deviation
of these values are 25.5 and 3.01, respectively. Assuming that these 11 automobiles can be considered a simple
random sample of cars of this model, which of the following is a correct statement?
 3.01 

 11 
A) A 95% confidence interval for  is 25.5  2.228 
 3.01 

 11 
B) A 95% confidence interval for  is 25.5  2.201
 3.01 

 10 
 3.01 
D) A 95% confidence interval for  is 25.5  2.201

 10 
C) A 95% confidence interval for  is 25.5  2.228 
E) The results cannot be trusted; the sample is too small.
6. The lengths of individual shellfish in a population of 10,000 shellfish are approximately normally distributed with
mean 10 centimeters and standard deviation 0.2 centimeter. Which of the following is the shortest interval that
contains approximately 4,000 shellfish lengths?
A) 0 cm to 9.949 cm
B) 9.744 cm to 10 cm
C) 9.744 cm to 10.256 cm
D) 9.895 cm to 10.105 cm
E) 9.9280 cm to 10.080 cm
7. A random sample has been taken from a population. A statistician, using this sample, needs to decide whether
construct a 90 percent confidence interval for the population mean or a 95 percent confidence interval for the
population mean. How will these intervals differ?
A) The 90 percent confidence interval will not be as wide as the 95 percent confidence interval.
B) The 90 percent confidence interval will be wider than the 95 percent confidence interval.
C) Which interval is wider will depend on how large the sample is.
D) Which interval is wider will depend on whether the sample is unbiased.
E) Which interval is wider will depend on whether a z-statistic or a t-statistic is used.
8. A quality control inspector must verify whether a machine that packages snack foods is working correctly. The
inspector will randomly select a sample of packages and weigh the amount of snack food in each. Assume that the
weights of food in packages filled by this machine have a standard deviation of 0.30 ounce. An estimate of the mean
amount of snack food in each package must be reported with 99.6 percent confidence and a margin of error of no
more than 0.12 ounce. What would be the minimum sample size for the number of packages the inspector must
select?
A) 8
B) 15
C) 25
D) 52
E) 60
9. An engineer for the Allied Steel Company has the responsibility of estimating the mean carbon content of a particular
day's steel output, using a random sample of 15 rods from that day's output. The actual population distribution of
carbon content is not known to be normal, but graphic displays of the engineer's sample results indicate that the
assumption of normality is not unreasonable. The process is newly developed, and there are no historical data on the
variability of the process. In estimating this day's mean carbon content, the primary reason the engineer should use a tconfidence interval rather than a z-confidence interval is because the engineer
A) is estimating the population mean using the sample mean
B) is using the sample variance as an estimate of the population variance
C) is using data, rather than theory, to judge that the carbon content is normal
D) is using data from a specific day only
E) has a small sample, and a z-confidence interval should never be used with a small sample
10. A simple random sample produces a sample mean, x , of 15. A 95 percent confidence interval for the corresponding
population mean is 15  3. Which of the following statements must be true?
A) Ninety-five percent of the population measurements fall between 12 and 18.
B) Ninety-five percent of the sample measurements fall between 12 and 18.
C) If 100 samples were taken, 95 of the sample means would fall between 12 and 18.
D) P(12  x  18) = 0.95
E) If  = 19, this x of 15 would be unlikely to occur.
11. A student working on a history project decided to find a 95 percent confidence interval for the difference in mean age
at the time of election to office for former American Presidents versus former British Prime Ministers. The student
found the ages at the time of election to office for the members of both groups, which included all of the American
Presidents and all of the British Prime Ministers, and used a calculator to find the 95 percent confidence interval based
on the t-distribution. This procedure is not appropriate in this context because
A) the sample sizes for the two groups are not equal
B) the entire population was measured in both cases, so the actual difference in means can be computed and a
confidence interval should not be used
C) elections to office take place at different intervals in the two countries, so the distribution of ages cannot be the
same
D) ages at the time of election to office are likely to be skewed rather than bell-shaped, so the assumptions for using
this confidence interval formula are not valid
E) ages at the time of election to office are likely to have a few large outliers, so the assumptions for using this
confidence interval formula are not valid
12. By what factor (approximately) will the margin of error for the value of a population proportion increase if we
increase the confidence level from 95% to 98%?
A) 0.43
B) 0.98
C) 1.19
D) 1.68
E) 2.33
13. A 95% confidence interval of the mean hourly salary of part-time lifeguards at public swimming pools in a particular
county during the summer is (5.65, 7.45). Which of the following are correct conclusions of this confidence interval?
I. There is a 95% probability that the mean hourly salary of all lifeguards in the county is in this confidence
interval.
II. The mean of the sample is $6.55.
III. 95% of all confidence intervals from samples of the same size will contain the mean hourly salary of all
lifeguards in the county.
A) I only
B) I and III
C) II and III
D) I, II, and III
E) III only
14. A CEO of a small corporation wishes to hire your consulting firm to conduct a simple random sample of its customers
to determine the proportion that consider her company as their primary source of her product. She tells your staff that
she requires that the margin of error in the proportion be no more than 3% with 95% confidence. Earlier studies have
indicated that the approximate proportion is 37%. What is the minimum size of the sample that you would
recommend to meet the requirements of your client if you use the earlier results?
A) 697
B) 748
C) 999
D) 1,407
E) No sample of any size will meet the requirements.
15. Which of the following describes a correct effect on the width of a confidence interval?
I. As sample size increases, the width of the confidence interval decreases.
II. As the confidence level increases, the width of the confidence interval increases.
III. As the standard error of the estimate increases, the width of the confidence interval increases.
A) I only
B) II only
C) I and III
D) II and III
E) I, II, and III
16. As sample size increases, if all other information stays the same, which of the following effects is reasonable?
A) The margin of error increases.
B) The margin of error decreases.
C) The confidence level increases.
D) The confidence level decreases.
E) None of these is affected by sample size.
17. A CEO of a small corporation wishes to hire your consulting firm to conduct a simple random sample of its customers
to determine the proportion that consider her company as their primary source of her product. She tells your staff that
she requires that the margin of error be no more than 3% with 95% confidence. Earlier studies have indicated that the
approximate proportion is 37%. Using the CEO's research, your staff calculates that a sample size of 995 or more will
meet her requirements. By how many more people would you increase the sample size if you use the most
conservative estimate of the sample proportion?
A) 12
B) 52
C) 73
D) 112
E) 1,068
18. One of the formulas for the margin of error for the estimate of a population mean uses a critical value from the normal
distribution corresponding to the level of confidence that we wish in the margin of error. Of those listed, which
quantity is automatically required to use this formula?
A) the appropriate t-value
B) the null hypothesis
C) the sample standard deviation
D) an estimate of the population standard deviation
E) the mean of the sample
19. Two investigators are arguing over what estimate to use to calculate the sample size for a study that they wish to
conduct of a population proportion. They have agreed to the same margin of error and the same confidence level.
However, investigator A wishes to use .30 for the estimated sample proportion based on his analysis of previous
studies while investigator B wishes to use .41 as the estimate based on her analysis of the earlier studies and some
evidence regarding trends in their industry. What is the ratio of the sample size of investigator A to the sample size of
investigator B?
A) 0.5
B) 0.686
C) 0.868
D) 0.945
E) 1.15
20. The sample size for a proposed study is calculated using the most conservative estimate of the sample proportion and a
margin of error of 3% with 95% confidence. Which of the following numbers best approximates the factor by which
the original sample size would have to be multiplied in order to reduce the margin of error to 1% with 95%
confidence?
A) 3
B) 4
C) 8
D) 9
E) 16
21. A random sample of 55 senior citizens in a retirement community indicated that 42 felt that there were not enough
overnight excursions available through the community. Which of the following is a valid conclusion based on this
information?
A) The 95% confidence interval is approximately (0.651, 0.876).
B) If 3 more seniors had voted that there were not enough trips, the width of the 95% confidence interval would
decrease by approximately 0.02.
C) There is not sufficient information to calculate a confidence interval.
D) This situation does not satisfy the assumptions and therefore, a confidence interval should not be calculated.
E) None of these is a valid conclusion.
22. A news program stated that one of the candidates for mayor of a certain city commissioned a popularity study to
ascertain his chances of re-election. The report claimed that 55% of the voters randomly sampled in this study favored
the incumbent; it also detailed that there was a margin of error of 3% with 95% confidence. Which of the following
best describes the meaning of this margin of error?
A) 3% of the time, the result of 55% will be wrong.
B) There is a probability of 3% that the sample is biased in favor of the incumbent.
C) There is a probability of 97% that 55% is the true value.
D) It is likely that the true percentage is within ±1.96 x 3% of the 55%.
E) It is likely that the true percentage is within 3% of the 55%.
23. An AP Statistics class performs a simulation in which each of the students roll a die 10 times and calculates the mean
and standard deviation of the values that occur. Based on these values, each student computes the 99% confidence
interval of the mean. Which of the following statements is a valid conclusion from this simulation?
A) There is a 99% probability that any one of the confidence intervals will contain the true mean of the values.
B) There is a 99% probability that all of the confidence intervals will contain the true mean of the values.
C) Approximately 99% of the confidence intervals calculated by the students will contain the true mean of the values.
D) Confidence comes from the 99% probability that the true mean will be in any of the intervals.
E) None of these statements is to be expected.
24. Which of the following is true about the margin of error in a sample?
I. The margin of error depends on the level of confidence desired in the sample results.
II. The margin of error depends on the sample mean that is found in the sample data.
III. The margin of error decreases as sample size increases.
A) I only
B) I and II
C) I and III
D) III only
E) I, II, and III
25. The sample size for a proposed study is calculated using the most conservative estimate of the sample proportion and a
margin of error of 3% with 95% confidence. Which of the following numbers best approximates the factor by which
the original sample size would have to be multiplied in order to maintain the margin of error at 3% but with 99%
confidence?
A) 1.7
B) 2.5
C) 3.4
D) 5.2
E) 8.3
26. In a simple random survey of 89 teachers of high school AP Statistics, 73 said that it was the most satisfying, most
enjoyable course they ever taught. Establish a 98% confidence interval estimate for the proportion of all high school
AP Statistics teachers who feel this way.
A) 0.820 ± 0.004
B) 0.820 ± 0.041
C) 0.820 ± 0.084
D) 0.820 ± 0.095
E) 0.820 ± 0.223
27. A catch of five fish of a certain species yielded the following ounces of protein per pound of fish: 3.1, 3.5, 3.2, 2.8,
and 3.4. What is a 90% confidence interval estimate for ounces of protein per pound of this species of fish?
A) 3.2 ± 0.202
B) 3.2 ± 0.247
C) 3.2 ± 0.261
D) 4.0 ± 0.202
E) 4.0 ± 0.247
28. A plant manager wishes to determine the difference in number of accidents per day between two departments. How
many days' records should be examined to be 90% certain of the difference in daily averages to within 0.25 accidents
per day? Assume standard deviations of 0.8 and 0.5 accidents per day the two departments, respectively
A) 39
B) 55
C) 78
D) 109
E) 155
29. A survey was conducted to determine the percentage of parents who would support raising the legal driving age to 18.
The results were stated as 67% with a margin of error of ±3%. What is meant by ±3%?
A) Three percent of the population were not surveyed.
B) In the sample, the percentage of parents who would support raising the driving age is between 64% and 70%.
C) The percentage of the entire population of parents who would support raising the driving age is between 64% and
70%.
D) It is unlikely that the given sample proportion result could be obtained unless the true percentage was between
64% and 70%.
E) Between 64% and 70% of the population were surveyed.
30. A social scientist wishes to determine the difference between the percentage of Los Angeles marriages and the
percentage of New York marriages that end in divorce in the first year. How large a sample (same for each group)
should be taken to estimate the difference to within ± 0.07 at the 94% confidence level?
A) 181
B) 361
C) 722
D) 1083
(E) 1443
31. A 95% confidence interval for the mean increase in sound pressure levels in pens of cattle exposed to low-level
military flights was calculated to be (84.5, 108.2) decibels. Which of the following statements is true?
A) The process used for this calculation has a probability of 0.95 of delivering an interval containing the true mean.
B) The probability that the true mean is between 84.5 and 108.2 is 0.95.
C) The probability that the next flight will raise the decibel levels between 84.5 and 108.2 dB is 0.95.
D) 0.95 of the increases in sound pressure levels are in the range, 84.5 to 108.2.
E) None of these is correct.
32. An analyst, using a random sample of n = 500 families, obtained a 90% confidence interval for mean monthly family
income for a large population: $600  $800. If the analyst had used a 99% confidence coefficient instead, the
confidence interval would be:
A) narrower and would involve a larger risk of being incorrect.
B) wider and would involve a smaller risk of being incorrect.
C) narrower and would involve a smaller risk of being incorrect.
D) wider and would involve a larger risk of being incorrect.
E) wider but it cannot be determined whether the risk of being incorrect would be larger or smaller.
33. Suppose a 95% confidence interval is computed for  resulting in the interval (112.4, 121.6). Which of the following
statements is correct?
A) 95% of the time, it falls within the interval (112.4, 121.6)
B) there is a 95% chance that falls within the interval (112.4, 121.6)
C) 95% of all possible values of fall within the interval (112.4, 121.6)
D) 95% of all possible samples produce an interval that does capture 
E) None of the above are true.
34. Complete the following with increases, decreases, remains the same.
a) as sample n increases, the confidence interval _______________________________
b) as the margin of error increases, the standard deviation __________________________________
c) as confidence increases, the sample size ______________________ in order to maintain the same margin of error.
d) if the bound (allowable error) increases, the confidence interval _____________________________
e) as confidence increases, the standard deviation _______________________
f) as confidence level increases, the margin of error ___________________________
ANSWERS
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
29
30.
31.
32.
33.
34.
E
B
C
C
A
D
A
D
B
E
B
C
C
C
E
B
C
D
C
D
B
E
C
C
A
D
C
A
B
B
E
B
D
a. decreases
b. increases
c. increases
d. increases
e. remains the same
f. increases