# Review for 1 sample CI Name. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

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1 Review for 1 sample CI Name MULTIPLE CHOICE. Choose the oe alterative that best completes the statemet or aswers the questio. Fid the margi of error for the give cofidece iterval. 1) A survey foud that 69% of a radom sample of 1024 America adults approved of cloig edagered aimals. Fid the margi of error for this survey if we wat 90% cofidece i our estimate of the percet of America adults who approve of cloig edagered aimals. A) 4.27% B) 2.38% C) 2.83% D) 24.35% E) 5.09% 2) A recet poll of 1500 ew home buyers foud that 60% hired a movig compay to help them move to their ew home. Fid the margi of error for this poll if we wat 99% cofidece i our estimate of the percet of ew home buyers who hired movers. A) 1% B) 6.52% C) 4.96% D) 0.5% E) 3.26% Use the give degree of cofidece ad sample data to costruct a cofidece iterval for the populatio proportio. 3) Of 346 items tested, 12 are foud to be defective. Costruct a 98% cofidece iterval for the percetage of all such items that are defective. A) (0.13%, 6.80%) B) (1.85%, 5.09%) C) (0.93%, 6.00%) D) (3.34%, 3.59%) E) (1.18%, 5.76%) 4) A survey of 300 uio members i New York State reveals that 112 favor the Republica cadidate for goveror. Costruct a 98% cofidece iterval for the percetage of all New York State uio members who favor the Republica cadidate. A) (30.1%, 44.5%) B) (17.8%, 56.8%) C) (31.9%, 42.8%) D) (30.8%, 43.8%) E) (26.7%, 47.9%) Solve the problem. 5) A pollster wishes to estimate the true proportio of U.S. voters who oppose capital puishmet. How may voters should be surveyed i order to be 95% cofidet that the true proportio is estimated to withi 3%? A) 752 B) 1068 C) 1842 D) 1503 E) Not eough iformatio is give. 6) A uiversityʹs admiistrator proposes to do a aalysis of the proportio of graduates who have ot foud employmet i their major field oe year after graduatio. I previous years, the percetage averaged 13%. He wats the margi of error to be withi 4% at a 99% cofidece level. What sample size will suffice? A) 469 B) 19 C) 563 D) E) 272 1

2 Provide a appropriate respose. 7) I a survey of 1,000 televisio viewers, 40% said they watch etwork ews programs. For a 90% cofidece level, the margi of error for this estimate is 2.5%. If we wat to be 95% cofidet, how will the margi of error chage? A) Sice more cofidece requires a more arrow iterval, the margi of error will be smaller. B) Sice more cofidece requires a more arrow iterval, the margi of error will be larger. C) Sice more cofidece requires a wider iterval, the margi of error will be smaller. D) Sice more cofidece requires a wider iterval, the margi of error will be larger. E) There is ot eough iformatio to determie the effect o the margi of error. Usig the t-tables, software, or a calculator, estimate the critical value of t for the give cofidece iterval ad degrees of freedom. 8) 90% cofidece iterval with df = 4. A) B) C) D) E) Iterpret the cofidece iterval. 9) Aalysis of a radom sample of 250 Illiois urses produced a 95% cofidece iterval for the mea aual salary of \$42,803 < μ(nurse Salary) < \$49,692. A) If we took may radom samples of Illiois urses, about 95% of them would produce this cofidece iterval. B) We are 95% cofidet that the average urse salary i the U.S. is betwee \$42,803 ad \$49,692. C) We are 95% cofidet that the iterval from \$42,803 to \$49,692 cotais the true mea salary of all Illiois urses. D) About 95% of Illiois urses ear betwee \$42,803 ad \$49,692. E) About 95% of the urses surveyed ear betwee \$42,803 ad \$49,692. Provide a appropriate respose. 10) You wat to determie if the average gas price i your city has exceeded \$2.15 per gallo for regular gas. You take a radom sample of prices from 8 gas statios, recordig the followig prices: \$2.13, \$2.10, \$1.80, \$2.09, \$2.17, \$2.12, \$2.10, \$2.11. Have the coditios ad assumptios for iferece bee met? A) No, the sample is ot radom. B) No, the sample is ot represetative. C) Yes, all coditios ad assumptios have bee met. D) No, the sample is more tha 10% of the populatio. E) No, the early ormal coditio is ot met. 11) How may upopped kerels are left whe you pop a bag of microwave popcor? Each day, quality cotrol persoel take a radom sample of 50 bags of popcor. They pop each bag i a microwave ad the cout the umber of upopped kerels. Have the coditios ad assumptios for iferece bee met? A) Yes, all coditios ad assumptio are met. B) No, the sample is more tha 10% of the populatio size. C) No, this is ot a represetative sample sice the quality cotrol persoel work for the compay ad are biased. D) No, the sample does ot meet the Nearly Normal coditio. E) No, the sample is ot likely to be represetative. Use the give sample data to costruct the idicated cofidece iterval for the populatio mea. 12) = 10, x = 13.7, s = 4.4 Fid a 95% cofidece iterval for the mea. A) (10.60, 16.80) B) (10.60, 16.83) C) (10.57, 16.83) D) (11.15, 16.25) E) (10.55, 16.85) 2

3 13) A savigs ad loa associatio eeds iformatio cocerig the checkig accout balaces of its local customers. A radom sample of 14 accouts was checked ad yielded a mea balace of \$ ad a stadard deviatio of \$ Fid a 98% cofidece iterval for the true mea checkig accout balace for local customers. A) (\$453.56, \$874.72) B) (\$492.52, \$835.76) C) (\$455.65, \$835.76) D) (\$455.65, \$872.63) E) (\$493.71, \$834.57) Use the give sample data to costruct the idicated cofidece iterval for the populatio mea. 14) The pricipal radomly selected six studets to take a aptitude test. Their scores were: Determie a 90% cofidece iterval for the mea score for all studets. A) (82.90, 72.27) B) (72.37, 82.80) C) (82.80, 82.80) D) (82.80, 72.37) E) (72.27, 82.90) SHORT ANSWER. Write the word or phrase that best completes each statemet or aswers the questio. A statistics professor asked her studets whether or ot they were registered to vote. I a sample of 50 of her studets (radomly sampled from her 700 studets), 35 said they were registered to vote. 15) Fid a 95% cofidece iterval for the true proportio of the professorʹs studets who were registered to vote. (Make sure to check ay ecessary coditios ad to state a coclusio i the cotext of the problem.) 16) Explai what 95% cofidece meas i this cotext. 17) What is the probability that the true proportio of the professorʹs studets who were registered to vote is i your cofidece iterval? 18) Accordig to a September 2004 Gallup poll, about 73% of 18- to 29-year-olds said that they were registered to vote. Does the 73% figure from Gallup seem reasoable for the professorʹs class? Explai. 19) If the professor oly kew the iformatio from the September 2004 Gallup poll ad wated to estimate the percetage of her studets who were registered to vote to withi ±4% with 95% cofidece, how may studets should she sample? The coutries of Europe report that 46% of the labor force is female. The Uited Natios woders if the percetage of females i the labor force is the same i the Uited States. Represetatives from the Uited States Departmet of Labor pla to check a radom sample of over 10,000 employmet records o file to estimate a percetage of females i the Uited States labor force. 20) The represetatives from the Departmet of Labor wat to estimate a percetage of females i the Uited States labor force to withi ±5%, with 90% cofidece. How may employmet records should they sample? 21) They actually select a radom sample of 525 employmet records, ad fid that 229 of the people are females. Create the cofidece iterval. 22) Iterpret the cofidece iterval i this cotext. 23) Explai what 90% cofidece meas i this cotext. 3

4 24) Should the represetatives from the Departmet of Labor coclude that the percetage of females i their labor force is lower tha Europeʹs rate of 46%? Explai. A professor at a large uiversity believes that studets take a average of 15 credit hours per term. A radom sample of 24 studets i her class of 250 studets reported the followig umber of credit hours that they were takig: 25) Fid a 95% cofidece iterval for the umber of credit hours take by the studets i the professorʹs class. Iterpret your iterval. Textbook authors must be careful that the readig level of their book is appropriate for the target audiece. Some methods of assessig readig level require estimatig the average word legth. Weʹve radomly chose 20 words from a radomly selected page i Stats: Modelig the World ad couted the umber of letters i each word: 5, 5, 2, 11, 1, 5, 3, 8, 5, 4, 7, 2, 9, 4, 8, 10, 4, 5, 6, 6 26) For a more defiitive evaluatio of readig level the editor wats to estimate the textʹs word legth to withi 0.5 letters with 98% cofidece. How may radomly selected words does she eed to use? 4

5 Aswer Key Testame: UNTITLED1 1) B 2) E 3) E 4) D 5) B 6) A 7) D 8) D 9) C 10) E 11) A 12) E 13) A 14) B 15) We have a radom sample of less tha 10% of the professorʹs studets, with 35 expected successes (registered) ad 15 expected failures (ot registered), so a Normal model applies. = 50, p^ = = 0.70, q^ = 1 - p^ = 0.30, so SE(p^) = Our 95% cofidece iterval is: p^q^ = (0.70)(0.30) 50 p^ ± z*se(p^) = 0.70 ± 1.96(0.065) = 0.70 ± = to = We are 95% cofidet that betwee 57.3% ad 82.7% of the professorʹs studets are registered to vote. 16) If may radom samples were take, 95% of the cofidece itervals produced would cotai the actual percetage of the professorʹs studets who are registered to vote. 17) There is o probability ivolved-oce the iterval is costructed, the true proportio of the professorʹs studets who were registered to vote is i the iterval or it is ot. 18) The 73% figure from Gallup seems reasoable sice 73% lies i our cofidece iterval. pq 19) ME = z* 0.04 = 1.96 (0.73)(0.27) = (1.96) 2(0.73)(0.27) = = 474 (0.04)2 Note: Sice there are oly 700 studets i the professorʹs class, she caot sample this may studets without violatig the 10% coditio! p^q^ 20) ME = z* 0.05 = = (0.46)(0.54) (0.46)(0.54) 0.05 = They should sample at least 269 employmet records. 5

6 Aswer Key Testame: UNTITLED1 21) We have a radom sample of less tha 10% of the employmet records, with 229 successes (females) ad 296 failures (males), so a Normal model applies. p^q^ = 525, p^ = ad q^ = 0.564, so SE(p^) = = (0.436)(0.564) = margi of error: ME = z* SE(p^) =(1.645)(0.022) = Cofidece iterval: p^ ± ME = ± or (0.3998, ) 22) We are 90% cofidet that betwee 40.0% ad 47.2% of the employmet records from the Uited States labor force are for females. 23) If may radom samples were take, 90% of the cofidece itervals produced would cotai the actual percetage of all female employmet records i the Uited States labor force. 24) No. Sice 46% lies i the cofidece iterval, (0.3998, ), it is possible that the percetage of females i the labor force matches Europeʹs rate of 46% females i the labor force. 25) With the coditios satisfied (from Problem 1), we ca fid a t-iterval for mea credit hours. We kow: = 24, y = 16.6, ad s = So, SE(y) = = Our cofidece iterval has the form y ± t* = 16.6 ± 0.94, or to s. We have t* 23 = Our 95% cofidece iterval is the 16.6 ± We are 95% cofidet that the iterval to cotais the true mea umber of credit hours that studets i the professorʹs class are takig. 26) First Estimate: ME = z* SE(y) 0.5 = = Although ot ecessary, sice 157 is quite large, we could fid a better estimate usig t*140 = 2.353, from Table T. ME = t*140 SE(y) 0.5 = =

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