ap stats chapter 7 b, Exercises of Mathematics

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vad AP Statistics Name. Key Chapter 7 Practice Test Date. 4 Hour. 17.4. A study of voting chose 663 registered voters at random shortly after an election. Of these, 72% said they had voted in the election. Election records show that only 56% of registered voters 2s voted i in the election. Which of the following statements is true about the boldface numbers? (a) 72% is a sample; 56% is a population. a } tf (b) 72% and 56% are both statistics. P-sT2 slabshe (Ce is a statistic and 56% is a parameter. . porameber 72% is a parameter and 56% is a statistic. (e) 72% and 56% are both parameters. T7.2. The Gallup Poll has decided to increase the size of its random sample of voters from about 1500 people to about 4000 people right before an election. The poll is designed to estimate the proportion of voters who favor a new law banning smoking in public buildings. The effect of this increase is to (a) reduce the bias of the estimate. Samp}< Si2< S$ poe { (b) increase the bias of the estimate. ei ne He. | sal bes ob an eshingle @educe the variability of the estimate. by ) larger St mpl w \ re ! (d) increase the variability of the estimate. (e) have no effect since the population size is the same. @” eshi imal Me vetrwabit. ly of 4 p T7.3. Suppose we select an SRS of size n = 100 from a large population having proportion p of successes. Let-6ep be the proportion of successes in the sample. For which value of p would it be safe to use the Normal approximation to the sampling distribution of Sep? YP 710 aa n (lp) 2)0 (a) 0.01 a 2 2 (b) 1/14 is Mhe enly loo ee ie ow 216 ae ule Pe i aa we (e) 0.999 1604.4 pr Lapa te pz Pre PS 44 17.4. The central limit theorem is important in statistics because it allows us to use the Normal distribution to make inferences concerning the population mean . Ccly ts wet heeded ben a) jf the sample size is reasonably large (for any population). ww if the population is Normally distributed and the sample size is reasonably large. Orginal a ste ba Ss (c) if the population is Normally distributed (for any sample size). Norms] ‘ duly: Fed bey a (d) if the population is Normally distributed and the population variance is known (for any sample size). s ample (e) if the population size is reasonably large (whether the population distribution is known or not). , Many yt heegt Worme ,, SCONE T7.5. The number of undergraduates at Johns Hopkins University is approximately 2000, while the number at Ohio State University is approximately 40,000. At both schools, a simple random sample of about 3% of the undergraduates is taken. Each sample is used to estimate the proportion p of all students at that university who own an iPod. Suppose that, in fact, p = 0.80 at both schools. Which of the following is the best conclusion? (a) The estimate from Johns Hopkins has less sampling variability than that from Ohio State. Corre estimate from Johns Hopkins has more sampling variability than that from Ohio State. The two estimates have about the same amount of sampling variability. (d) It is impossible to make any statement about the sampling variability of the two estimates since the students re ee aren Sola Hephas Ohe Shale N) 22060 N= 46 ceo The larger dhe sample Sre SRS 2. 63(Qvoe) SAS>.63 (4.000) dh smaller dhe varigh: lids ial 1 Suen Fic. bo, h2|Qooe Pave Srey a yan 17.6. A researcher initially plans to take an SRS of size n froma population that has mean 80 and standard deviation 20. If he were to double his sample size (to 2n), the standard deviation of the sampling distribution of the sample mean would be multiplied by (a) V2 On, ££: o£ Os oak i a ae | % dar "gore 2, : sy (he 4) avn V3 | (d) 5 2 LL OF n The student newspaper at a large university asks an SRS of 250 undergraduates, “Do you favor eliminating the carnival from the term-end celebration?” All in all, 150 of the 250 are in favor. Suppose that (unknown to you) 55% of all undergraduates favor eliminating the carnival. If you took a very large number of SRSs of size n = 250 from this population, the sampling distribution of the sample proportion6ep would be > a (a) exactly Normal with mean 0.55 and standard deviation 0.03. e P= SS N-DSG Garproximately Normal with mean 0.55 and standard deviation 0.03. Ai exactly Normal with mean 0.60 and standard deviation 0.03. aA P “p 2. s¢ 4d) approximately Normal with mean 0.60 and standard deviation 0.03. ‘ (e) heavily skewed with mean 0.55 and standard deviation 0.03. Oyz (550645) V7 Normal , 2500.58) 710 ond 950(.45) 2) 0 Wo «67.03 ne 7 Ip) 2 fe, e210 and hl lp) 210 B25 2m 11,5210 tof_ 1olase) & PoP onder Dad, 17.8. Which of the following statements about the sampling distribution of the sample mean ie{incorrect?> Pe (6) The standard deviation of the sampling distribution will decrease as the sample size increases. aoe () The standard deviation of the sampling distribution is a measure of the variability of the sample mean among repeated samples. Thy, (€) The sample mean is an unbiased estimator of the true population mean. wed (d) The sampling distribution shows how the sample mean will vary in repeated samples. ‘rec (eyThe sampling distribution shows how the sample was distributed around the sample mean. fal. The Seumpliney Aish buen hes In face) on about hew the Semple Mean Varies doves Scmole Jo Scumple Web whad any Sample self looks Lie T7.9. A machine is designed to fill 16-ounce bottles of shampoo. When the machine is working properly, the mean amount poured into the bottles is 16.05 ounces with a standard deviation of 0.1 ounce. Assume that the machine is working properly. If four bottles are randomly selected each hour and the number of ounces in each bottle is measured, then 95% of the observations should occur in which interval? ven Yo of the observations s 16.05 to 16.15 ounc ~ rs -0.30 te +0.30 ounces We ane med Jatd She Ashebbun is Mormel an) Shee (c) 15.95 to 16.15 ounces n2 uy the CLT daly (leywone to 16.20 ounces None of the above 7 - Remevakes 0 & Normal Dishn hohin GS-/o of dad falls wYun 2 shar J os lanabur 17.10. Suppose that you are a student aide in the library and agree to be paid according to the “random pay” system. Each week, the librarian flips a coin. If the coin comes up heads, your pay for the week is $80. If it comes up tails, your pay for the week is $40. You work for the library for 100 weeks. Suppose we choose an SRS of 2 weeks and calculate your average earnings X. The shape of the sampling distribution of X will be x (a) Normal. 2 a 0 8 (b) approximately Normal. nz9 i $5 H $0.7 386 = $50 (c) right-skewed. Te $46 < 1 346 “7 d to (d) left-skewed T dy @pymmetric but not Normal o B—fro —» su, 2 Sine Mere Gre onl 4 toll eb be Morme |, POet be ovbeurns, = ive —79 40 2)What is the shape of the sampling distribution of X? Justify your answer. Sn MO is 2 2, by CUT, sep Isbibdien of X jg ee Vorme/. 4) Find the probability that the average fee paid by the sample of households exceeds $29, Show your work. ~N( 95, ayn) _ - P(x Zaq) rormed (34, oP NPIS o1aq JS ex “Ther IS book a lay *f oh eustee. [a — = 4 0g of Jedony a Scumple ad SOlo MS ih ghey th. Qv0rage Po | peu) he Ve Tabecnet then £54 1%. 15. According to government data, 22% of American children under the age of six live in households with incomes less than the official poverty level. A study of learning in early childhood chooses an SRS of 300 Ses children, Find the probability that more than 20% of the sample are from poverty households. Be sure to check that you can use the Normal approximation. 1s More Sime SRS n2300 gyi th pra “pt ps fo} J teen cond Bans Op 2] LM a voy lo(3ee) S pop de deen wie, sad . 3006 6 pop reasonable Jy as5ume V Nornal Condon a “ ° PC > 7,30) = normed t {56 > 300 (49 210 an) Bol.) 7 6 1-9, 0934 ) «2 we 1342) y B44 7 . o> = ” Sammplny dshibohor a Sample pas Preprcn is “M099, 0930) 02 4 “Thee. % about a BO-b chance Shad Se I 7 a fo ane. a np o 500 chideen wll el) nee “ Duele whe Ihe és households with iacemes bs the Ye ise poweby ao