STA 223 Test #3 Prctice Multiple Choice 1. A newspper conducted sttewide survey concerning the 1998 rce for stte sentor. The newspper took rndom smple (ssume it is n SRS) of 12 registered voters nd found tht 62 would vote for the Republicn cndidte. Let p represent the proportion of registered voters in the stte tht would vote for the Republicn cndidte. A 9% confidence intervl for p is A).517 ±.14. B).517 ±.24. C).517 ±.28. D).517 ±.249. 2. After once gin losing footbll gme to the rch rivl, college's lumni ssocition conducted survey to see if lumni were in fvor of firing the coch. An SRS of 1 lumni from the popultion of ll living lumni ws tken. 64 of the lumni in the smple were in fvor of firing the coch. Let p represent the proportion of ll living lumni who fvor firing the coch. A 95% confidence intervl for p is A).64 ±.79. B).64 ±.94. C).64 ±.124. D).64 ±.36. 3. In formulting hypotheses for sttisticl test of significnce, the null hypothesis is often A) sttement of "no effect" or "no difference." B) the probbility of observing the dt you ctully obtined. C) sttement tht the dt re ll. D).5. 4. In their dvertisements, the mrketers of new diet progrm would like to clim tht their methods result in men weight loss of more thn 1 pounds in two weeks. In order to determine if this is vlid clim, they hire n independent testing gency which then selects 25 people to be plced on this diet. The gency should be testing the null hypothesis : 1 nd the lterntive hypothesis A) : < 1. B) : > 1. C) : 1. D) σ : 1 ±. n 5. A resercher wishes to determine if the mjority of Americn dults over the ge of 65 pln to vote Republicn in the net presidentil election. Let p represent the proportion of the popultion of ll Americn dults over the ge of 65 who pln to vote Republicn in the net presidentil election. In terms of p, the resercher should test which of the following null nd lterntive hypotheses. A) : p. 5 vs. : p >. 5. B) : p. 5 vs. : p. 5 C) : p. 5. vs. : p <. 5 D) : p. 5 most polls.. vs. : p.5 ±. 3, since.3 is the mrgin of error for 1
6. The men re of the severl thousnd prtments in new development is dvertised to be 125 squre feet. A tennt group thinks tht the prtments re smller thn dvertised. They hire n engineer to mesure smple of prtments to test their suspicion. The pproprite null nd lterntive hypotheses, nd, for re A) : 125 nd : 125. B) : 125 nd : < 125. C) : 125 nd : > 125. D) cnnot be specified without knowing the size of the smple used by the engineer. 7. The P-vlue of test of null hypothesis is A) the probbility, ssuming the null hypothesis is true, tht the test sttistic will tke vlue t lest s etreme s tht ctully observed. B) the probbility, ssuming the null hypothesis is flse, tht the test sttistic will tke vlue t lest s etreme s tht ctully observed. C) the probbility tht the null hypothesis is true. D) the probbility tht the null hypothesis is flse. 8. In testing hypotheses, which of the following would be strong evidence ginst the null hypothesis? A) using smll level of significnce. B) using lrge level of significnce. C) obtining dt with smll P-vlue. D) obtining dt with lrge P-vlue. 9. In sttisticl test of hypotheses, we sy the dt re sttisticlly significnt t level α if A) α.5. B) α is smll. C) the P-vlue is less thn α. D) the P-vlue is lrger thn α. 1. The weights (in pounds) of three dult mles re 16, 215, nd 195. The stndrd error of the men of these three weights is A) 63.33. B) 19.. C) 16.7. D) 13.12. 11. The heights (in inches) of mles in the U.S. re believed to be normlly distributed with men. The verge height of rndom smple of 25 Americn dult mles is found to be 69.72 inches nd the stndrd devition of the 25 heights is found to be S 4.15. The stndrd error of is A).17. B).69. C).83. D) 2.4. 2
12. Scores on the SAT Mthemtics test (SAT-M) re believed to be normlly distributed with men. The scores of rndom smple of three students who recently took the em re 55, 62, nd 48. A 95% confidence intervl for bsed on these dt is A) 55. ± 173.9. B) 55. ± 142. C) 55. ± 128.58. D) 55. ± 15.1. 13. An SRS of 1 postl employees found tht the verge time these employees hd worked for the postl service ws 7 yers with stndrd devition S 2 yers. Assume the distribution of the time the popultion of employees hve worked for the postl service is pproimtely norml with men. Are these dt evidence tht hs chnged from the vlue of 7.5 yers of 2 yers go? To determine this we test the hypotheses : 7.5 : 7.5 using the one-smple t test. The pproprite degrees of freedom for this test re A) 9. B) 1. C) 99. D) 1. 14. An SRS of 1 postl employees found tht the verge time these employees hd worked for the postl service ws 7 yers with stndrd devition S 2 yers. Assume the distribution of the time the popultion of employees hve worked for the postl service is pproimtely norml with men. Are these dt evidence tht hs chnged from the vlue of 7.5 yers of 2 yers go? To determine this we test the hypotheses : 7.5 : 7.5 using the one-smple t test. The P-vlue for the one-smple t test is A) lrger thn.1. B) between.1 nd.5. C) between.5 nd.1. D) below.1. 3
15. An SRS of 1 postl employees found tht the verge time these employees hd worked for the postl service ws 7 yers with stndrd devition S 2 yers. Assume the distribution of the time the popultion of employees hve worked for the postl service is pproimtely norml with men. Are these dt evidence tht hs chnged from the vlue of 7.5 yers of 2 yers go? To determine this we test the hypotheses : 7.5 : 7.5 using the one-smple t test. Suppose we re not sure if the popultion distribution is norml. In which of the following circumstnces would use of the t procedure s bove yield misleding results? A) A histogrm of the dt shows some skewness. B) A stem plot of the dt hs smll outlier. C) The smple stndrd devition is lrge. D) None of the bove. 16. We wish to see if the dil indicting the oven temperture for certin model oven is properly clibrted. Four ovens of this model re selected t rndom. The dil on ech is set to 3 F nd fter one hour the ctul temperture of ech is mesured. The tempertures mesured re 35, 31, 3, nd 35. Assuming tht the ctul tempertures for this model when the dil is set to 3 re normlly distributed with men, we test whether the dil is properly clibrted by testing the hypotheses : 3 : 3. Bsed on the dt, the vlue of the one-smple t sttistic is A) 5. B) 4.9. C) 2.45. D) 1.23. 4
Use the following to nswer questions #17 nd #18: Bgs of certin brnd of tortill chips clim to hve net weight of 14 ounces. Net weights ctully vry slightly from bg to bg nd re normlly distributed with men. A representtive of consumer dvocte group wishes to see if there is ny evidence tht the men net weight is less thn dvertised nd so intends to test the hypotheses : 14 : < 14. To do this, he selects 16 bgs of this brnd t rndom nd determines the net weight of ech. e finds the smple men to be 13.82 nd the smple stndrd devition to be S.24. 17. Bsed on the bove dt, we would conclude A) we would reject t significnce level.1 but not t.5. B) we would reject t significnce level.5 but not t.25. C) we would reject t significnce level.25 but not t.1. D) we would reject t significnce level.1. 18. Referring to the bove dt, suppose we were not sure if the distribution of net weights ws norml. In which of the following circumstnces would we not be sfe using t procedure in this problem? A) The men nd medin of the dt re nerly equl. B) A histogrm of the dt shows moderte skewness. C) A stem plot of the dt hs lrge outlier. D) The smple stndrd devition is lrge. 19. You re thinking of using t -procedure to test hypotheses bout the men of popultion using significnce level of.5. You suspect the distribution of the popultion is not norml nd my be modertely skewed. Which of the following sttements is correct? A) You should not use the t -procedure since the popultion does not hve norml distribution. B) You my use the t -procedure provided your smple size is lrge sy, t lest 5. C) You my use the t -procedure, but you should probbly only clim the significnce level is.1. D) You my not use the t -procedure. t -procedures re robust to nonnormlity for confidence intervls but not for tests of hypotheses. 2. To estimte, the men slry of full professors t Americn colleges nd universities, you obtin the slries of rndom smple of 4 full professors. The smple men is $7322 nd the smple stndrd devition is A) 7322 ± 1144. B) 7322 ± 572. C) 7322 ± 431. D) 7322 ± 28.6. S $44. A 99% confidence intervl for is 5
21. The college newspper of lrge Midwestern university periodiclly conducts survey of students to determine cmpus ttitudes on vriety of issues. Pictures of the students interviewed re printed in the pper long with quotes of their responses. Students re interviewed by reporter "roming" the cmpus who selects students to interview "hphzrdly." On prticulr dy the reporter interviews five students nd sks them if they feel there is dequte student prking on cmpus. Four of the students sy no. The proportion pˆ who respond "no" is thus.8, nd the stndrd error SE ( pˆ ) of the proportion is A).8. B).64. C).18. D).32. 22. A rdio tlk show host with lrge udience is interested in the proportion p of dults in his listening re tht think the drinking ge should be lowered to 18. To find this out he poses the following question to his listeners. "Do you think tht the drinking ge should be reduced to 18 in light of the fct tht 18-yer-olds re eligible for militry service?" e sks listeners to phone in nd vote "yes" if they gree the drinking ge should be lowered nd "no" if not. You re told tht the proportion pˆ of those who phoned in nd nswered yes is pˆ.7 nd the stndrd error SE ( pˆ ) of the proportion is.459. The number of people who phoned in A) is 5. B) is 1. C) is 2. D) cnnot be determined from the informtion given. 23. A rdio tlk show host with lrge udience is interested in the proportion p of dults in his listening re tht think the drinking ge should be lowered to 18. To find this out he poses the following question to his listeners. "Do you think tht the drinking ge should be reduced to 18 in light of the fct tht 18-yer-olds re eligible for militry service?" e sks listeners to phone in nd vote "yes" if they gree the drinking ge should be lowered nd "no" if not. Of the 1 people who phoned in 7 nswered "yes." Which of the following ssumptions for inference bout proportion using confidence intervl re violted? A) The dt re n SRS from the popultion of interest. B) The popultion is t lest 1 times s lrge s the smple. C) n is so lrge tht both the count of successes nˆ p nd the count of filures n( 1 pˆ ) re 1 or more. D) There pper to be no violtions. 24. 8 rts whose mothers were eposed to high levels of tobcco smoke during pregnncy were put through simple mze. The mze required the rts to mke choice between going left or going right t the outset. 6 of the rts went right when running the mze for the first time. Assume tht the 8 rts cn be considered n SRS from the popultion of ll rts born to mothers eposed to high levels of tobcco smoke during pregnncy (note tht this ssumption my or my not be resonble, but reserchers often ssume lb rts re representtive of such lrger popultions since lb rts re often bred to hve very uniform chrcteristics). The stndrd error for the proportion pˆ of those who went right the first time when running the mze is A).23. B).484. C).548. D).559. 6
25. An inspector inspects lrge trucklods of pottoes to determine the proportion p in the shipment with mjor defects prior to using the pottoes to mke potto chips. Unless there is cler evidence tht this proportion is less thn.1 she will reject the shipment. To rech decision she will test the hypotheses : p.1 : p <.1 using the lrge smple test for popultion proportion. To do so, she selects n SRS of 5 pottoes from the more thn 2 pottoes on the truck. Suppose tht only 2 of the pottoes smpled re found to hve mjor defects. The P-vlue of her test is A).427. B).793. C).154. D) less thn.2. 26. An inspector inspects lrge trucklods of pottoes to determine the proportion p in the shipment with mjor defects prior to using the pottoes to mke potto chips. Unless there is cler evidence tht this proportion is less thn.1 she will reject the shipment. To rech decision she will test the hypotheses : p.1 : p <.1 using the lrge smple test for popultion proportion. To do so, she selects n SRS of 5 pottoes from the more thn 2 pottoes on the truck. Suppose tht only 2 of the pottoes smpled re found to hve mjor defects. Which of the following ssumptions for inference bout proportion using hypothesis test re violted? A) The dt re n SRS from the popultion of interest. B) The popultion is t lest 1 times s lrge s the smple. C) n is so lrge tht both np nd n( 1 p ) re 1 or more, where p is the proportion with mjor defects if the null hypothesis is true. D) There pper to be no violtions. 27. A newspper conducted sttewide survey concerning the 1998 rce for governor. The newspper took rndom smple (ssume it is n SRS) of 12 registered voters nd found tht 64 would vote for the Democrtic cndidte. Is this evidence tht cler mjority of the popultion would vote for the Democrtic cndidte? To nswer this, test the hypotheses The P-vlue of your test is A).492. B).33. C).14. D) less thn.2. : p.5 : p >.5. 7
28. A sociologist is studying the effect of hving children within the first two yers of mrrige on the divorce rte. Using hospitl birth records, she selects rndom smple of 2 couples who hd child within the first two yers of mrrige. Following up on these couples, she finds tht 8 couples re divorced within five yers. A 9% confidence intervl for the proportion of couples who hd child within the first two yers of mrrige nd re divorced within five yers is A).4 ±.35. B).4 ±.44. C).4 ±.57. D).4 ±.68. 29. A sociologist is studying the effect of hving children within the first two yers of mrrige on the divorce rte. Using hospitl birth records, she selects rndom smple of 2 couples who hd child within the first two yers of mrrige. Following up on these couples, she finds tht 8 couples re divorced within five yers. To determine if hving children within the first two yers of mrrige increses the divorce rte over n estblished 3 percent for mrried couples in generl, we should A) test the hypotheses : p. 5, : p. 5. B) test the hypotheses : p. 5, : p >. 5. C) test the hypotheses : p. 4, : p >. 4. D) None of the bove. 3. A rdio tlk show host with lrge udience is interested in the proportion p of dults in his listening re tht think the drinking ge should be lowered to 18. To find this out he poses the following question to his listeners. "Do you think tht the drinking ge should be reduced to 18 in light of the fct tht 18 yer olds re eligible for militry service?" e sks listeners to phone in nd vote "yes" if they gree the drinking ge should be lowered nd "no" if not. Of the 1 people who phoned in 7 nswered "yes." Which of the following ssumptions for inference bout proportion using confidence intervl re violted? A) The dt re n SRS from the popultion of interest. B) The popultion is t lest 1 times s lrge s the smple. C) n is so lrge tht both the count of successes nˆ p nd the count of filures n(1 - pˆ ) re 1 or more. D) There pper to be no violtions. ANSWER KEY: 1. B 2. B 3. A 4. B 5. A 6. B 7. A 8. C 9. C 1. C 11. C 12. A 13. C 14. C 15. D 16. C 17. D 18. C 19. B 2. B 21. C 22. B 23. A 24. B 25. B 26. C 27. C 28. C 29. D 3. A 8