Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
CHAPTER 22 GROUP QUIZ 1. TWO CONFIDENCE INTERVAL ESTIMATES FROM THE SAME SAMPLE ARE (16.4, 29.8) AND (14.3,31.9). WHAT IS THE SAMPLE MEAN, AND IF ONE ESTIMATE IS AT THE 95% LEVEL WHILE THE OTHER IS AT THE 99% LEVEL, WHICH IS WHICH? A A. = 23.1; (16.4, 29.8) is the 95% level. B. = 23.1; (16.4, 29.8) is the 99% level. C. It is impossible to completely answer this question without knowing the sample size. D. It is impossible to completely answer this question without knowing the sample standard deviation. E. It is impossible to completely answer this question without knowing the sample size and standard deviation. 2. HOSPITAL ADMINISTRATORS WISH TO LEARN THE AVERAGE LENGTH OF STAY OF ALL SURGICAL PATIENTS. A STATISTICIAN DETERMINES THAT, FOR A 95% CONFIDENCE LEVEL ESTIMATE OF THE AVERAGE LENGTH OF STAY TO WITHIN +0.5 DAYS, 50 SURGICAL PATIENTS’ RECORDS WILL HAVE TO BE EXAMINED. HOW MANY RECORDS SHOULD BE LOOKED AT TO OBTAIN A 95% CONFIDENCE LEVEL ESTIMATE TO WITHIN +0.25 DAYS? A. 25 B. 50 C. 100 D. 150 E. 200 E 3. THE NUMBER OF ACCIDENTS PER DAY AT A LARGE FACTORY IS NOTED FOR EACH OF 64 DAYS. ASSUME Σ = 1.52. WITH WHAT DEGREE OF CONFIDENCE CAN WE ASSERT THAT THE MEAN NUMBER ACCIDENTS PER DAY AT THE FACTORY IS BETWEEN 3.2 AND 3.96? A. 48% B. 63% C. 90% D. 95% E. 99% D 4. A MANUFACTURER WISHES TO DETERMINE THE LIST PRICE FOR A SMOKE DETECTOR. A SURVEY OF THE LIST PRICE OF SIMILAR SMOKE DETECTORS SOLD BY NINE OTHER COMPETING COMPANIES SHOWED AN AVERAGE LIST PRICE OF $10.95 WITH A STANDARD DEVIATION OF $1.49. FIND A 95% CONFIDENCE INTERVAL FOR THE AVERAGE LIST PRICE FOR A SMOKE DETECTOR. (ASSUME ALL CONDITIONS ARE MET) A. Between $9.98 and $11.92 B. Between $9.80 and $12.10 C. Between $9.98 and $12.07 D. None of these B 5. A SURVEY OF THE HOSPITAL RECORDS OF 25 RANDOMLY SELECTED PATIENTS SUFFERING FROM A PARTICULAR DISEASE INDICATED THAT THE AVERAGE LENGTH OF STAY IN THE HOSPITAL IS 10 DAYS. THE STANDARD DEVIATION IS ESTIMATED TO BE 2.1 DAYS. THE CRITICAL VALUE NEEDED FOR FINDING A 95% CONFIDENCE INTERVAL WOULD BE WHICH OF THE FOLLOWING: A. t* = 2.064 C. z* = 1.960 B. t* = 2.060 D. none of these A 6. IT IS BELIEVED THAT USING A NEW FERTILIZER WILL RESULT IN A YIELD OF 1.6 TONS PER ACRE. A BOTANIST CARRIES OUT A TWO-TAILED TEST ON A FIELD OF 64 ACRES. DETERMINE THE P-VALUE IF THE MEAN YIELD PER ACRE IN THE SAMPLE IS 1.72 TONS WITH A STANDARD DEVIATION OF 0.4. WHAT IS THE CONCLUSION? A. P = .0097, so the claim should be rejected at 1%, 5%, and 10% significance levels. B. P = .0193, so the claim should be rejected at the 10% and 5% levels but not at the 1% level. C. P = .0097, so the claim should be rejected at the 10% level but not at the 5% and 1% levels. D. P = .0193, so the claim should be rejected at the 1% level but not at the 10% and 5% levels. E. P = .0097, and so there is not enough evidence to reject the claim at any of the three levels. B 7. AN AUTHOR OF A NEW BOOK CLAIMS THAT ANYONE FOLLOWING HIS SUGGESTED DIET PROGRAM WILL LOSE AN AVERAGE OF 2.8 POUNDS PER WEEK. A RESEARCHER BELIEVES THAT THE TRUE FIGURE WILL BE LOWER AND PLANS A TEST INVOLVING A RANDOM SAMPLE OF 36 OVERWEIGHT PEOPLE. SHE WILL REJECT THE AUTHOR’S CLAIM IF THE MEAN WEIGHT LOSS IN THE VOLUNTEER GROUP IS LESS THAN 2.5 PER WEEK. ASSUME THAT THE STANDARD DEVIATION AMONG ALL INDIVIDUALS IS 1.2 POUNDS PER WEEK. IF THE TRUE MEAN VALUE IS 2.4 POUNDS PER WEEK, WHAT IS THE POWER OF THE TEST? A B C D E B 8) The Clements HS website claims that the average SAT math score is 617. We believe that the average score is higher. We plan to survey 200 students and intend to speak up if their average score is at least 630. Suppose the true average score is 620 with a standard deviation of 75. What is the probability of making a Type II error? Power 630 620 P( x 630) P z 0.03 75 / 200 TypeII 0.97 630 620 P( x 630) P z 0.97 75 / 200 9. GIVEN: WITH A SAMPLE SIZE OF 21 AND A KNOWN POPULATION STANDARD DEVIATION. IF THE TEST STATISTIC = 1.9. WHAT IS THE P-VALUE? A. 0.03597 C. 0.05743 B. 0.0287 D. 0.0719 C 10. GIVEN: WITH A SAMPLE SIZE OF 28 AND AN UNKNOWN Σ. IF THE TEST STATISTIC = 1. WHAT IS THE PVALUE? A. 0.1629 C. 0.1587 B. 0.3262 D. 0.1631 D 11. THE LABEL ON THE PACKAGE OF CORDS CLAIMS THAT THE BREAKING STRENGTH OF A CORD IS 3.5 LBS, BUT A HARDWARE STORE OWNER BELIEVES THE REAL VALUE IS LESS. SHE PLANS TO TEST 36 SUCH CORDS; IF THE MEAN BREAKING STRENGTH IS LESS THAN 3.25 LBS, SHE WILL REJECT THE CLAIM ON THE LABEL. IF THE STANDARD DEVIATION FOR THE BREAKING STRENGTHS OF ALL SUCH CORDS IS 0.9 LBS, WHAT IS THE PROBABILITY OF MISTAKENLY REJECTING A TRUE CLAIM? A. 0.05 C. 0.15 B. 0.10 D. 0.45 E. 0.94 A 12) City planners are trying to decide among various parking plan options. Before making a decision they wish to test the claim that shoppers park for an average of 47 minutes in the downtown area. The planners have decided to tabulate parking durations for 225 shoppers and reject the claim if the sample mean exceeds 50 minutes. If the claim is actually wrong and the true mean is 51 minutes, what is the probability that planners will mistakenly fail to reject the false claim? Assume the standard deviation in parking durations is 27 min. 50 47 A. P z 27 225 D. 50 51 P z 27 225 B. E. 50 47 Pt 27 225 50 51 Pt 27 225 50 51 C. P z 27 225