Review for Chapter 9

Transcription

1 Review for Chapter 9 1. For which of the followig ca you use a ormal approximatio? a) = 100, p =.02 b) = 60, p =.4 c) = 20, p =.6 d) = 15, p = 2/3 e) = 10, p =.7 2. What is the probability of a sample of 10 studets gettig a average score of 510 or more o a stadardized test if the test scores are ormally distributed with a mea of 505 ad a stadard deviatio of 50? a).6241 b).4601 c).3745 d).1587 e) No way to determie this 3. Samples of size 49 are draw from a distributio that's highly skewed to the right with a mea of 70 ad a stadard deviatio of 14. What is the probability of gettig a sample mea betwee 71 ad 73? a) 0 b) c).0563 d).2417 e) No way to determie this 4. Which of the followig statemets are true? I. The larger the sample the larger the spread i the samplig distributio II. Provided that the populatio size is sigificatly greater tha the sample size, the spread of a samplig distributio is about the same o matter what the populatio size III. Bias has to do with the ceter, ot the spread of a samplig distributio. a) I ad II b) I ad III c) II ad III d) I, II, ad III e) Noe of the above statemets are true 5. Which of the followig statemets are true I. The samplig distributio of p (hat) has a mea equal to the populatio proportio p. II. The samplig distributio of p (hat) has a stadard deviatio equal to p( 1 III. The samplig distributio of p (hat) is cosidered close to ormal provided that 30 a) I ad II b) I ad III c) II ad III d) I, II, ad III e) Noe of the above 1

2 6. Which of the followig are true? I. A samplig distributio of a statistic cosists of all possible radom samples of the same size from a give populatio II. Regardless of the shape of the origial populatio, for samples of size 2, x ad x III. Uless there was extreme skewess or outliers, we ca assume that a samplig distributio of a sample mea was approximately ormal for samples of size 40. a) I oly b) II oly c) III oly d) I ad III oly e) I, II ad III 7. Which aswer shows: a) x = p b) x = 1. The mea of the distributio x 2. The stadard deviatio of the distributio of x 3. The mea of the distributio of p (hat) 4. The stadard deviatio of the distributio of p (hat) c) x = x = d) x = p x = x p(hat) = x p(hat) = x p(hat) = p p(hat) = p ( 1 p ( 1 p(hat) = p p(hat) = p ( 1 p ( 1 p(hat) = p p(hat) = p( 1 e) x = p x = p( 1 p(hat) = p( 1 p(hat) = p ( 1 8. Which of the followig statemets are true I. Sample parameters are used to make ifereces about populatios statistics. II. Statistics from smaller samples have more variability. III. Parameters are fixed, while statistics vary depedig o which sample is chose. a) I ad II b) I ad III c) II ad III d) I, II, ad III e) Noe of the above statemets are true. 2

3 9. Which of the followig statemets are true I. The samplig distributio of x has a stadard deviatio 3 eve if the populatio is ot ormally distributed II. The samplig distributio of x is ormal if the populatio has a ormal distributio III. Whe is large, the samplig distributio of x is approximately ormal eve if the populatio is ot ormally distributed. a) I ad II b) I ad III c) II ad III d) I, II, ad III e) Noe of the above statemets are true. 10. Which of the followig statemets are true I. The mea of the set of sample meas varies iversely as the square root of the size of the samples. II. The variace of the set of sample meas varies directly as the size of the samples ad iversely as the variace of the origial populatio. III. The stadard deviatio of the set of sample meas varies directly as the stadard deviatio of the origial populatio ad iversely as the square root of the size of the samples. a) I oly b) II oly c) III oly d) I ad II e) I ad III 11. Which of the followig statemets are ubiased estimators for the correspodig populatio parameters I. Sample meas II. Sample proportios III. Sample stadard deviatio IV. Sample size a) Noe are ubiased b) I ad II c) I ad III d) III ad IV e) All are ubiased 12. Suppose that 35% of all busiess executives are willig to switch compaies if offered a higher salary. If a headhuter radomly cotacts a SRS of 100 executives, what is the probability that over 40% will be willig to switch compaies if offered a higher salary? a).1469 b).1977 c).4207 d).8023 e) Give that 58% of all gold dealers believe ext year will be a good oe to speculate i South Africa gold cois, i a SRS of 150 dealers, what is the probability that betwee 55% ad 60% believe that it will be a good year to speculate? a).0500 b).1192 c).3099 d).4619 e).9215

4 14. The average outstadig bill for deliquet customer accouts for a atioal departmet store chai is $ with a stadard deviatio of $ I a SRS of 50 deliquet accouts, what is the probability that the mea outstadig bill is over $200? a).0526 b).0667 c).4090 d).5910 e) The average umber of daily emergecy room admissios at a hospital is 85 with a stadard deviatios of 37. I a SRS of 30 days, what is the probability that the mea umber of daily emergecy admissios is betwee 75 ad 95? a).1388 b).2128 c).8612 d).8990 e) True or False: A samplig distributio of the mea retiremet age i North America ca cosist of as few as 100 sample values. 17. Cosider drawig samples of size 2 from {A, B, C, D, E} ad computig the mea of each sample. The samplig distributio would cosist of how may values? a) 10 b) 5 c) 3 d) 100 e) Samples of size 10 are draw from a large (N > 10,000), symmetric populatio with a mea of 45 ad a stadard deviatio of 9. What are the mea ad stadard deviatio of the samplig distributio of the mea for samples of size 10, ad what s the shape of the distributio? a) mea = 45, std. dev. = The sample size is small, so the shape will be skewed b) mea = 45, std. dev. = The sample size is small, so the shape will resemble the paret populatio (symmetric about its mea) c) mea = 45, std. dev. = The sample size is small, so the shape will resemble the paret populatio (symmetric about its mea) d) mea = 45, std. dev. = The sample size is small, so the shape will be skewed e) mea = 45, std. dev. = The sample size is large, so the shape will resemble the paret populatio (symmetric about its mea) 19. A populatio has proportio.35 of some characteristic of iterest. What are the mea ad stadard deviatio of the samplig distributio of p-hat for samples of size 50? What s the shape of the samplig distributio of p-hat? a) mea =.25, std. dev. =.023. The shape appears as a uiform deisty curve. b) mea =.35, std. dev. =.067. Not eough iformatio to determie shape. c) mea =.25, std. dev. =.023. The shape is skewed right. d) mea =.35, std. dev. =.067. The shape is skewed left. e) mea =.35, std. dev. =.067. Samples of =50 are relatively large, so the shape is approximately ormal. 20. True or False: The Cetral Limit Theorem tells us that the samplig distributio of a sample mea will be approximately ormal regardless of the shape of the paret populatio. 4

5 21. We create a samplig distributio of x-bar by takig samples of size 70 from a populatio whose mea is kow to be 5 ad whose stadard deviatio is 1. What ca we say about the samplig distributio of x-bar? a) We eed iformatio o the paret populatio to determie a aswer. b) The Cetral Limit Theorem does ot apply. c) Because is large, the Cetral Limit Theorem applies d) You ca say that the shape of the samplig distributio of x-bar will be approximately ormal eve though you have o ifo o the shape of the paret populatio. e) Both c ad d 22. True of False: (Refer to the previous exercise) The mea of x-bar is 5 ad the stadard deviatio of x-bar is.12; the last two facts would be true regardless of the shape of the origial distributio or the sample size. 23. A popular soda comes i 12-oz cas. However, the actual volume of soda i the ca varies ormally with a mea of 11.9 oz ad a stadard deviatio of.3 oz. What s the probability that the mea amout of soda i a six-pack is less tha 12 oz? a).082 b).207 c).793 d).652 e) Refer to #24: What s the probability that the mea amout of soda i a six-pack is betwee 11.7 oz ad 12 oz? a).096 b).258 c).793 d).752 e) The probability of wiig at roulette is about.474. Suppose you bet 50 times. What s your probability of beig eve or ahead after 50 bets? a).36 b).64 c).78 d).52 e) Refer to #26: What s your probability of beig eve or ahead after 1,000 bets? a).09 b).95 c).05 d).75 e) Which of the followig are true? I. A samplig distributio of a statistic cosists of all possible radom samples of the same size from a give populatio. II. Regardless of the shape of the origial populatio, for samples of size 2, ad X X III. Uless there was extreme skewess or outliers, we ca assume that a samplig distributio of a sample mea was approximately ormal for samples of size 40. a) I oly b) II oly c) III oly d) I ad III oly e) I, II, ad III 5

6 Chapter 10 Practice Problems 1. The stadard deviatio of SAT scores is 100 poits. A researcher decides to take a sample of 500 studets' scores to estimate the mea score of studets i your state. What is the stadard deviatio of the sample mea? A. 0.2 B C. 5 D. 100 E. Ca't determie without the sample mea 2. The 99.7% cofidece iterval for the mea legth of frog jumps is (12.64 cm, cm). Which of the followig statemets is a collect iterpretatio of 99.7% cofidece? A. Of the total umber of frogs i your area of the coutry, 99.7% ca jump betwee cm ad cm. B. There is a 99.7% chace that the true mea legth of frog jumps falls betwee cm ad cm. C. If we were to repeat this samplig may times, 99.7% of the cofidece itervals we could costruct would cotai the true populatio mea. D. 99.7% of the cofidece itervals we could costruct after repeated samplig would go from cm to cm E. There's a 99.7% chace that ay particular frog I catch ca jump betwee cm ad cm. 3. True or False: A 95% cofidece iterval is arrower tha a 90% cofidece iterval for the same data set. 4. What's the critical z-value for a 85% cofidece iterval? A B C D. Ca't be determied without kowig the populatio stadard deviatio E. Ca't be determied without kowig the sample size 5. What's z* for a 78% cofidece iterval? A..77 B C D E. Caot compute without the stadard deviatio. 6. A researcher computes a 90% cofidece iterval for the mea weight (i lb) of widgets produced i a factory. The iterval is (7.2, 8.9). Which of these is a correct iterpretatio of this iterval? A. Out of all the widgets produced i all widget factories, 90% weigh betwee 7.2 ad 8.9 lb. B. We ca be 90% cofidet that all the widgets weigh betwee 7.2 ad 8.9 lb C. There's a 90% chace the populatio value is betwee 7.2 ad 8.9 lb. D. Niety percet of all sample meas are equivalet to the true mea weight of all the widgets. E. If you drew may samples of size ad costructed a cofidece iterval from each sample, 90% of the itervals would cotai the true populatio value. 7. A teacher admiisters a stadardized math test to his class of 75 studets. The mea score (out of 300 possible poits) is 235. From previous studies, you kow the populatio stadard deviatio is 28. Usig the sample data give, calculate a 95% cofidece iterval for the populatio mea, A. (234.1,235.9) B. (226.7, 243.3) C. (228.7,241.3) D. (233.0, 237.0) E. (200.0, 300.0) 6

7 Questios 8-9 refer to the followig iformatio: A researcher is iterested i estimatig the mea blood alcohol cotet (BAC) of people arrested for drivig uder the ifluece. The sample cosists of 250 idividuals with a mea BAC of.145. Based o past data, the researcher assumes a populatio stadard deviatio of What's the margi of error for a 90% cofidece iterval i this sceario? A B C..107 D E. Not eough iformatio to compute the margi of error 9. What's the 95% cofidece iterval for the sceario above? A. (.137,.153) B. (.080,.210) C. (.138,.152) D. (.111,.172) E. Not eough iformatio to compute the iterval 10. A teacher admiisters a stadardized math test to his class of 75 studets. The mea score (out of 300 possible poits) is 235. From previous studies, you kow the populatio stadard deviatio is 28. The pricipal has decided that she wats to estimate the average score to withi 4 poits (margi of error = 4) with 99% cofidece. If she ca oly admiister the test to oe radom sample of studets, how large should this sample be to achieve the desired margi of error ad cofidece level? A. 75 studets B. 16 studets C. 188 studets D. 326 studets E. 325 studets 11. A radom sample of 85 adults foud that average calorie cosumptio was 2,100 per day. Previous research has foud a stadard deviatio of 450 calories, ad you use this value for. Costruct a 99% cofidece iterval for the populatio mea. A. (1,905.5,2,289.6) B. (2,004.4,2,195.6) C. (2,097.4,2,102.6) D. (1,650.0, 2,550.0) E. (1,974.3,2,225.7) 12. A radom sample of 85 adults foud that average calorie cosumptio was 2,100 per day. Previous research has foud a stadard deviatio of 450 calories, ad you use this value for. A researcher wats to estimate a 95% cofidece iterval ad is willig to accept a margi of error of 50 calories. She kows it will cost $50 to survey each member of the sample. Give this iformatio, how much will it cost to survey the miimum umber of people? A. $4,050 B. $26,870 C. $15,600 D. $3,750 E. $15,

8 13. Which of the followig statemets is true? A. Smaller sample sizes produce larger margis of error because smaller samples always have larger stadard deviatios. B. The poit estimate is the measure of variatio used i the computatio of the margi of error. C. Smaller sample sizes produce larger margis of error because smaller samples are more susceptible to radom variability. D. All of the above are correct. E. Noe of the above are correct. 14. Sulfur compouds cause off-odors i wie, so wiemakers wat to kow the odor threshold, the lowest cocetratio of a compoud that the huma ose ca detect. The odor threshold for dimethyl sulfide (DMS) i traied wie tasters is about 25 micrograms per liter of wie ( ). The utraied oses of cosumers may be less sesitive, however. Here are the DMS odor thresholds for 10 utraied studets: Assume that the stadard deviatio of the odor threshold for utraied oses is kow to be = 7. A. Fid z* for a 93% cofidece iterval for the true mea of the populatio. Show your work usig the graph provided. B. Costruct ad iterpret a 93% cofidece iterval for the mea DMS odor threshold amog all utraied studets. C. Nick explais that 93% cofidet meas that the process you used to calculate the cofidece iterval would result i a iterval that captures the sample mea i 93% of all possible samples of 10 utraied testers from the populatio. Commet o Nick s iterpretatio of the cofidece level. D. Determie the sample size you would eed to estimate µ withi at a 93% cofidece level. 15. About 42,000 high school studets took the AP Statistics exam i The free-respose sectio of the exam cosisted of five ope-eded problems ad a ivestigative task. Each free-respose questio is scored o a 0 to 4 scale (with 4 beig the best). A radom sample of 25 studet papers yielded the followig scores o oe of the freerespose questios: A. Is a sample of 25 papers large eough to provide a good estimate of the mea score of all 42,000 studets o this exam problem? Justify your aswer. B. Do you thik the populatio of scores o this questio is Normally distributed? Explai why or why ot. C. Costruct ad iterpret a 95% cofidece iterval for the mea score o this exam questio. Be sure to explai why it s okay to calculate the iterval i light of your aswer to Questio A ews article o a Gallup Poll oted that 28 percet of the 1548 adults questioed felt that those who were able to work should be take off welfare. The article also said, The margi of error for a sample size of 1548 is plus or mius three percetage poits. A. Opiio polls usually aouce margis of error for 95% cofidece. Usig this fact, explai to someoe who kows o statistics what margi of error plus or mius three percetage poits meas. B. Do you agree with the margi of error stated i the poll results? If so, explai why. If ot, tell why ot. C. What is the 99% cofidece iterval from this poll? Iterpret the iterval i cotext. D. What coditios must be met i order for the cofidece iterval i Questio 3 to be valid? Check whether each of those coditios is satisfied i this case. E. This poll was coducted by telephoe. Explai how udercoverage could lead to a biased estimate i this case. 8