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AP Stat Confidence Intervals Review
Multiple Choice Identify the choice that best completes the statement or answers the question.
____ 1. A level C confidence interval is A. any interval with margin of error ± C. B. an interval computed from sample data by a method that has probability C of producing an interval containing the true value of the parameter of interest. C. an interval with margin of error ± C that is also correct C % of the time. D. an interval computed from sample data by a method that guarantees that the probability the interval computed contains the parameter of interest is C. E. an interval computed from sample data that has probability (1 – C) of not containing the parameter of interest.
____ 2. A 95% confidence interval for the mean of a population is computed from a random sample and found to be
9 3. We may conclude that
A. there is a 95% probability that is between 6 and 12.
B. 95% of values sampled are between 6 and 12. C. if we took many, many additional random samples and from each computed a 95%
confidence interval for , approximately 95% of these intervals would contain .
D. there is a 95% probability that the true mean is 9 and a 95% chance that the true margin of error is 3. E. all of the above are true.
____ 3. The Gallup Poll interviews 1600 people. Of these, 18% say that they jog regularly. The news report adds: "The poll had a margin of error of plus or minus three percentage points." You can safely conclude that A. 95% of all Gallup Poll samples like this one give answers within ± 3 % of the true population value. B. the percent of the population who jog is certain to be between 15% and 21%. C. 95% of the population jog between 15% and 21% of the time. D. we can be 3% confident that the sample result is true. E. if Gallup took many samples, 95% of them would find that exactly 18% of the people in the sample jog.
____ 4. A polling organization announces that the proportion of American voters who favor congressional term limits is 64 percent, with 95% confidence and margin of error of 3 percent. This means that A. if the poll were conducted again in the same way, there is a 95% chance that the fraction of voters favoring term limits in the second poll would be between 61 percent and 67 percent. B. there is a 95% probability that the true percentage of voters favoring term limits is between 61 and 67 percent. C. if the poll were conducted again the same way, there is a 95% probability that the percentage of voters favoring term limits in the second poll would be within 3 percent of the percentage favoring term limits in the first poll. D. among 95% of the voters, between 61 percent and 67 percent favor term limits. E. none of the above.
____ 5. Use Scenario 8-1. The term “95% confidence” means we can be A. sure that between 44% and 50% of all Americans think we should have a third party. B. 95% confident that 47% of all Americans think we should have a third party.
C. 95% confident that between 44% and 50% of all Americans think we should have a third party. D. 95% confident that between 44% and 50% of the people interviewed think we should have a third party. E. between 93% and 97% confident that 47% of all Americans think we should have a third party.
Scenario 8- A 2008 Gallup poll found that 47% of adults 18 years old or older in the United States felt that a third political party is needed to represent the American people. In the description of methods, the poll takers said: “For results based on the total sample of national adults, one can say with 95% confidence that the maximum margin of sampling error is 3 percentage points.”
____ 6. Use Scenario 8-1. Among the poll respondents who identified their current party affiliation as “independent,” 63% agreed that we need a third political party. The margin of error for this result is A. less than ± 3%, because only some of the people in the sample were independents, so the sample size is smaller. B. greater than ± 3%, because only some of the people in the sample were independents, so the sample size is smaller. C. equal to ± 3%, because this result comes from the same sample survey. D. less than ± 3%, because only some of the population are independents, so it's easier to estimate facts about them. E. greater than ± 3%, because only some of the population are independents, so it's harder to estimate facts about them.
____ 7. The critical value used in a 95% confidence interval for a population proportion is A. the value in a standard Normal distribution such that 95% of the scores are above that value. B. the value in a standard Normal distribution such that 95% of the scores are less than that distance from 0. C. the value in a t -distribution such that 95% of the scores are above that value. D. the product of a value calculated from the standard Normal distribution for 95% and the standard error of the sample proportion. E. the average variability of the sample proportion in all samples of size n from the population.
____ 8. The critical value used to construct a confidence interval for a proportion depends upon A. The confidence level being used and the size of the sample. B. The size of the sample and the sample proportion. C. The confidence level, the size of the sample, and the standard deviation of the population. D. Only on the sample size. E. Only on the confidence level.
____ 9. A researcher studying reaction time of drivers states that, “A 95% confidence interval for the mean time it takes for a driver to apply the brakes after seeing the brake lights on a vehicle in front of him is 1.2 to 1. seconds. What are the point estimate and margin of error for this interval? A. Point estimate = 1.2 seconds; margin of error = 0.6 seconds. B. Point estimate = 1.2 seconds; margin of error = 0.3 seconds. C. Point estimate = 1.5 seconds; margin of error 95%. D. Point estimate = 1.5 seconds; margin of error = 0.6 seconds. E. Point estimate = 1.5 seconds; margin of error = 0.3 seconds.
C. Only source III. D. All three sources of error. E. None of these sources of error.
____ 16. Which of the following sources of error is included in the margin of error A. chance variation in choosing a random sample. B. undercoverage. C. some of the subjects did not understand the questions. D. voluntary response. E. all of the above.
____ 17. A website asks visitors to vote for which of several user-submitted videos is funniest. After a few days they have collected 250 votes, and they would like to construct a 95% confidence interval for the proportion of visitors who prefer one of the videos. However, they recognize that their sampling method involves voluntary response, so the data may be biased. How can they compensate for this problem when constructing their confidence interval? A. Use a lower confidence level, such as 80%. B. Use a higher confidence level, such as 99%. C. Collect an additional 250 or more votes using an SRS. D. Use a t -procedure instead of a z -procedure. E. Throw this data out…there is no way to compensate for this bias.
____ 18. A radio talk show host with a large audience is interested in the proportion of adults in his listening area
that think the drinking age should be lowered to 18. To find out, he poses the following question to his listeners: “Do you think that the drinking age should be reduced to 18 in light of the fact that 18-year-olds are eligible for military service?” He asks listeners to phone in and vote “yes” if they agree the drinking age should be lowered and “no” if not. Of the 100 people who phoned in, 70 answered “yes.” Which of the following assumptions for inference about a proportion using a confidence interval has been violated? A. The population is at least 10 times as large as the sample. B. C.
D. The data are an SRS from the population of interest. E. There appear to be no violations.
____ 19. A quality control inspector is testing microprocessor chips made during a single day by a new machine to determine the proportion of defective chips. She selects an SRS of 80 chips from the 3000 chips produced by the machine on that day. It turns out that six of the chips are defective. Which of the following conditions for constructing a confidence interval for the proportion of defective chips has been violated? A.
B. An SRS has been taken from the population of interest. C. The population is at least 10 times the size of the sample. D. The population is approximately Normally distributed. E. There appear to be no violations.
____ 20. You are told that the proportion p of those who answered "yes" to a poll about internet use is p = 0.70, and the standard error SEp of the proportion is 0.0459. The sample size was A. is 50. B. is 99. C. is 100. D. is 200.
E. cannot be determined from the information given.
____ 21. Eighty rats whose mothers were exposed to high levels of tobacco smoke during pregnancy were put through a simple maze. The maze required the rats make a choice between going left or going right at the outset. Sixty of the rats went right when running the maze for the first time. Assume that the eighty rats can be considered an SRS from the population of all rats born to mothers exposed to high levels of tobacco smoke during pregnancy. (Note that this assumption may or may not be reasonable, but researchers often assume lab rats are representative of such larger populations because lab rats are often bred to have very uniform characteristics.) The standard error for the proportion p of those who went right the first time when running the maze is A. 0.0023. B. 0.0072. C. 0.0484. D. 0.0548. E. 0.0559.
____ 22. A noted psychic was tested for ESP. The psychic was presented with 200 cards face down and asked to determine if the card featured one of five symbols: star, cross, circle, square, or three wavy lines. The psychic was correct in 48 cases. If p represents the proportion of correct guesses the psychic made, what is the standard error of p? A. 0. B. 0. C. 0. D. 0. E. 0.
Scenario 8- A newspaper conducted a statewide survey concerning the 2008 race for state senator. The newspaper took a random sample (assume it is an SRS) of 1200 registered voters and found that 620 would vote for the Republican candidate. Let p represent the proportion of registered voters in the state that would vote for the Republican candidate.
____ 23. Use Scenario 8-2. A 90% confidence interval for p is A. 0.517 ± 0.014. B. 0.517 ± 0.022. C. 0.517 ± 0.024. D. 0.517 ± 0.028. E. 0.517 ± 0.249.
____ 24. Use Scenario 8-2. Which of the following is closest to the sample size you would need in order to estimate p with margin of error 0.01 with 95% confidence? Use 0.5 as an approximation of p. A. 49 B. 1500 C. 4800 D. 4900 E. 9604
Scenario 8- After a college’s football team once again lost a football game to the college’s arch rival, the alumni association conducted a survey to see if alumni were in favor of firing the coach. An SRS of 100 alumni from the population of all living alumni was taken. Sixty-four of the alumni in the sample were in favor of firing the coach. Let p represent the proportion of all living alumni who favor firing the coach.
D. A 90% t - interval with 1 degree of freedom E. A 90% t - interval with 10 degrees of freedom
____ 31. Which of the following has the lowest probability? A. Selecting a random value above 1 from a t -distribution with 5 degrees of freedom. B. Selecting a random value above 1 from a standard Normal distribution. C. Selecting a random value above 2 from a t -distribution with 5 degrees of freedom. D. Selecting a random value above 2 from a t -distribution with 10 degrees of freedom. E. Selecting a random value above 2 from a standard Normal distribution.
____ 32. What is the critical value t * for a 90% confidence interval when n = 15? A. 1. B. 1. C. 1. D. 1. E. 2.
____ 33. What is the critical value t * for a 99% confidence interval when n = 20? A. 2. B. 2. C. 2. D. 2. E. 2.
____ 34. What proportion of scores in a t -distribution with 6 degrees of freedom are above t = 2.447? A. 0. B. 0. C. 0. D. 0. E. 0.
____ 35. The weights of a sample of three adult males are (in pounds) 160, 215, and 195. The standard error of the mean of these three weights is A. 190.00. B. 27.84. C. 22.73. D. 16.07. E. 9.28.
____ 36. The heights (in inches) of males in the United States are believed to be Normally distributed with mean . The average height of a random sample of twenty-five American adult males is found to be J = 69.72 inches and the standard deviation of the twenty-five heights is found to be s = 4.15. The standard error of J is A. 0.17. B. 0.69. C. 0.83. D. 1.856. E. 2.04.
____ 37. 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 ± 401.11.
B. 550.00 ± 173.88.
C. 550.00 ± 142.00.
D. 550.00 ± 128.58.
E. 550.00 ± 105.01.
____ 38. An SRS of 100 postal employees found that the average time these employees had worked for the postal service was J = 7 years with standard deviation s = 2 years. Assume the distribution of the time the population of employees have worked for the postal service is approximately Normal. A 95% confidence interval for the mean time the population of postal service employees have spent with the postal service is A. 7 ± 2. B. 7 ± 1.984. C. 7 ± 0.525. D. 7 ± 0.4. E. 7 ± 0.2.
____ 39. Do students tend to improve their SAT Mathematics (SAT-M) score the second time they take the test? A random sample of four students who took the test twice received the following scores.
Student 1 2 3 4 First Score^450 520 720 Second Score^440 600 720
Assume that the change in SAT-M score (second score first score. for the population of all students taking the test twice is approximately Normally distributed with mean . A 90% confidence interval for is A. (^) 25.0 118.03. B. (^) 25.0 64.29. C. (^) 25.0 47.56. D. (^) 25.0 43.08. E. (^) 25.0 33.24.
____ 40. To estimate , the mean salary of full professors at American colleges and universities, you obtain the salaries of a random sample of 400 full professors. The sample mean is and the sample standard deviation is s = $4400. A 99% confidence interval for is A. (^) $73,220 11,440. B. (^) $73,220 567. C. (^) $73,220 431. D. (^) $73,220 28.6. E. none of these.
____ 41. The heights of young American women, in inches, are approximately Normally distributed with mean and standard deviation = 2.4. If I want to construct a 99% confidence interval with a margin of error of no more than 1 inch, the smallest sample I can take is closest to A. 2. B. 7. C. 16. D. 38. E. 39.
E. 90% likely to contain the unknown mean math SAT score of all seniors in the district.
____ 47. An SRS of 100 postal employees found that the average time these employees had worked for the postal service was J = 7 years with standard deviation s = 2 years. Suppose we are not sure if the population distribution is normal. In which of the following circumstances would use of the t procedure yield misleading results? A. A histogram of the data shows moderate skewness. B. A stemplot of the data shows a uniform distribution. C. The sample standard deviation is large. D. A histogram of the data shows strong skewness. E. None of the above.
____ 48. Bags of a certain brand of tortilla chips claim to have a net weight of 14 ounces. A representative of a consumer advocate group wishes to see if there is any evidence that the mean net weight is less than advertised and plans to construct a 95% confidence interval for the mean, using an SRS of 16 bags. Suppose he is not sure if the distribution of net weights is Normal. In which of the following circumstances would he not be safe to use a t procedure? A. The mean and median of the data are nearly equal. B. A histogram of the data shows moderate skewness. C. A stemplot of the data has a large outlier. D. The sample standard deviation is large. E. None of these circumstances would prevent us from using t procedures.
____ 49. In checking conditions for constructing confidence intervals for a population mean, it’s important to plot the distribution of sample data. Below are dot plots describing samples from three different populations. For which of the three samples would it be safe to construct a t -interval?
A. Plot X only B. Plot Y only C. Plot Z only D. Plots Y and Z E. None of the plots.
____ 50. The scores of a certain population on the Wechsler Intelligence Scale for Children (WISC. are thought to be approximately Normally distributed. A simple random sample of 10 children from this population is taken, and each is given the WISC. The 95% confidence interval for the mean is computed from these scores. A histogram of the 10 WISC scores is given.
Based on this histogram, we would conclude that A. we can be 95% confident that the true mean WISC score in this population is in this interval. B. the 95% confidence interval computed from these data is not very reliable. C. the 95% confidence interval computed from these data should actually be considered a 99% confidence interval. D. the 95% confidence interval computed from these data should actually be considered a 90% confidence interval. E. only one student’s score should fall outside the 95% confidence interval.
42. D
43. C
44. C
45. B
46. D
47. E
48. C
49. D
50. B
