AP Stat Confidence Intervals Review, Exercises of Statistics

Download AP Stat Confidence Intervals Review and more Exercises Statistics in PDF only on Docsity! 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 8-1 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 1.8 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. 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. 0.0009 B. 0.0283 C. 0.0302 D. 0.0354 E. 0.4330 Scenario 8-2 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 8-3 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. ____ 25. Use Scenario 8-3. A 95% confidence interval for p is A. 0.64 ± 0.009. B. 0.64 ± 0.079. C. 0.64 ± 0.094. D. 0.64 ± 0.124. E. 0.64 ± 0.360. ____ 26. Use Scenario 8-3. Which of the following is closest to the sample size you would need to estimate p with a margin of error of 0.05 with 95% confidence? Use 0.5 as an approximation of p. A. 269 B. 385 C. 538 D. 768 E. 1436 Scenario 8-4 A sociologist is studying the effect of having children within the first two years of marriage on the divorce rate. Using hospital birth records, she selects a random sample of 200 couples that had a child within the first two years of marriage. Following up on these couples, she finds that 80 couples are divorced within five years. ____ 27. Use Scenario 8-4. A 90% confidence interval for the proportion p of all couples that had a child within the first two years of marriage and are divorced within five years is A. 0.40 ± 0.004. B. 0.40 ± 0.035. C. 0.40 ± 0.044. D. 0.40 ± 0.057. E. 0.40 ± 0.068. ____ 28. Use Scenario 8-4. Which of the following is closest to the sample size you would need to estimate p with a margin of error of 0.02 with 90% confidence? Use 0.4 from the first sample as an approximation of p. A. 24 B. 600 C. 1624 D. 2305 E. 3842 ____ 29. Using the same sample statistics, you calculate a 95% t-interval for a population mean and a 95% z-interval for a population mean. Which interval has a larger margin of error? A. The t-interval’s margin of error is larger. B. The z-interval’s margin of error is larger. C. The two intervals have the same margin of error. D. Which interval has the larger margin or error depends on the degrees of freedom for the z-interval. E. Which interval has the larger margin or error depends on the degrees of freedom for the t-interval. ____ 30. Which of the following confidence intervals has the largest critical value? A. A 95% z-interval B. A 95% t-interval with 1 degree of freedom C. A 95% t-interval with 10 degrees of freedom 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. 1.645 B. 1.753 C. 1.761 D. 1.960 E. 2.145 ____ 33. What is the critical value t* for a 99% confidence interval when n = 20? A. 2.086 B. 2.093 C. 2.576 D. 2.845 E. 2.861 ____ 34. What proportion of scores in a t-distribution with 6 degrees of freedom are above t = 2.447? A. 0.90 B. 0.10 C. 0.05 D. 0.025 E. 0.01 ____ 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. 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. AP Stat Confidence Intervals Review Answer Section MULTIPLE CHOICE 1. B 2. C 3. A 4. E 5. C 6. B 7. B 8. E 9. E 10. D 11. C 12. C 13. A 14. B 15. E 16. A 17. E 18. D 19. A 20. C 21. C 22. C 23. C 24. E 25. C 26. B 27. D 28. C 29. A 30. B 31. E 32. C 33. E 34. D 35. D 36. C 37. B 38. D 39. C 40. B 41. E