Test 12A AP Statistics Name: Directions: Work on these sheets. Answer completely, but be concise. Tables are attached.

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1 Test 12A AP Sttistics Nme: Directions: Work on these sheets. Answer completely, but be concise. Tbles re ttched. Prt 1: Multiple Choice. Circle the letter corresponding to the best nswer. 1. An opinion poll sks rndom smple of dults whether they fvor bnning ownership of hndguns by privte citizens. A commenttor believes tht more thn hlf of ll dults fvor such bn. The null nd lterntive hypotheses you would use to test this clim re () H ˆ.5; : ˆ : p = H p >. 5 (b) H ˆ.5; : ˆ : p = H p. 5 (c) H : p =.5; H : p. 5 (d) H : p = ; H : p > (e) None of the bove. The nswer is. 2. 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 μ. 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 H : μ = 14, H : μ < 14 To do this, he selects 16 bgs of this brnd t rndom nd determines the net weight of ech. He finds the smple men to be x = nd the smple stndrd devition to be s =.24. We conclude tht we would () reject H t significnce level.1 but not t.5. (b) reject H t significnce level.5 but not t.25. (c) reject H t significnce level.25 but not t.1. (d) reject H t significnce level.1. (e) fil to reject H t the α =.1 level. 3. A Type I error in the previous question would men () concluding tht the bgs re being underfilled when they ctully ren t. (b) concluding tht the bgs re being underfilled when they ctully re. (c) concluding tht the bgs re not being underfilled when they ctully re. (d) concluding tht the bgs re not being underfilled when they ctully ren t. (e) none of these 4. You re thinking of using t procedure to test hypotheses bout the men of popultion using significnce level of.5. You suspect tht the distribution of the popultion is not Norml nd my be modertely skewed. Which of the following sttements is correct? () You should not use the t procedure becuse the popultion does not hve Norml distribution. (b) You my use the t procedure if your smple size is lrge, sy, t lest 5. (c) You my use the t procedure, but you should probbly clim only tht the significnce level is.1. (d) You my not use the t procedure. The t procedures re robust to non-normlity for confidence intervls but not for tests of hypotheses. (e) You my use the t procedure if there re no outliers. Chpter 12 1 Test 12A

2 5. After once gin losing footbll gme to the rchrivl, 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. Suppose you wish to see if mjority of living lumni re in fvor of firing the coch. The pproprite test sttistic is () z = (.64.5) (.64)(.36) 1 (b) z = (.64.5) (.5)(.5) 1 (c) z = (.64.5) (.64)(.36) 64 (d) z = (.64.5) (.5)(.5) 64 (e) t = (.64.5) (.5)(.64) 1 6. We prefer the t procedures to the z procedures for inference bout popultion men becuse () z cn be used only for lrge smples. (b) z requires tht you know the popultion stndrd devition σ. (c) z requires tht you cn regrd your dt s n SRS from the popultion of interest. (d) z requires tht your popultion be Normlly distributed. (e) z requires tht your observtions be independent. 7. Looking online (for exmple, t espn.go.com) you find the slries of ll 22 plyers for the Chicgo Cubs s of opening dy of the 25 bsebll seson. The club totl ws $87 million, eighth in the mjor legues. Which inference procedure would you use to estimte the verge slry of the Cubs plyers? () one-smple z intervl for μ (b) one-smple t intervl for μ (c) one-smple t test (d) one-smple z test (e) none of these 8. You red in the report of psychology experiment tht seprte nlyses for our two groups of 12 prticipnts reveled no overll plcebo effect for our student group (men =.8, SD =.37, t(11) =.49) nd significnt effect for our non-student group (men =.35, SD =.37, t(11) = 3.28, p <.1). Are the two vlues given for the t test sttistic correct? (The null hypothesis is tht the men effect is zero.) () Yes, both re correct. (b) The t sttistic for the student group is correct, but the one for the non-student group is incorrect. (c) The t sttistic for the non-student group is correct, but the one for the student group is incorrect. (d) Both t sttistics re incorrect. (e) We cn t tell whether either t sttistic is correct, becuse we ren t given the ctul dt. Chpter 12 2 Test 12A

3 Prt 2: Free Response Communicte your thinking clerly nd completely. 9. In study of the effectiveness of weight-loss progrms, 47 subjects who were t lest 2% overweight took prt in group support progrm for 1 weeks. Privte weighings determined ech subject s weight t the beginning of the progrm nd 6 months fter the progrm s end. The pired t test ws used to ssess the significnce of the verge weight loss. The pper reporting the study sid, The subjects lost significnt mount of weight over time, t(46) = 4.68, P <.1. () Wht hypotheses were tested in this study? Be sure to define ny prmeters you use. (b) Discuss whether ech of the required conditions for using the pired t test is stisfied in this study. (c) The pper follows the trdition of reporting significnce only t fixed levels such s α =.1. In fct the results re more significnt thn P <.1 suggests. Wht is the P-vlue of this t test? (d) Explin to someone who knows no sttistics but is interested in weight-loss progrms wht the prcticl conclusion is. Chpter 12 3 Test 12A

4 1. Mrs Inc., mkers of M&M s cndies, clims tht they produce plin M&M s with the following distribution: Brown: 3% Red: 2% Yellow: 2% Ornge: 1% Green: 1% Blue: 1% A bg of plin M&M s ws selected rndomly from the grocery store shelf, nd the color counts were s follows: Brown: 16 Red: 11 Yellow: 19 Ornge: 5 Green: 7 Blue: 3 () You wnt to conduct n pproprite test of the mnufcturer s clim for the proportion of yellow M&M s. Identify the popultion nd prmeter of interest. Then stte hypotheses. (b) Stte nd verify the conditions for performing the significnce test. (c) Clculte the test sttistic nd the P-vlue. (d) Wht do you conclude bout the mnufcturer s clim? Explin. (e) Bsed on this smple, construct nd interpret 9% confidence intervl for the proportion of yellow M&M s cndies produced by Mrs. Chpter 12 4 Test 12A

5 Answers to Chpter 12 Prctice Test Multiple Choice: 1. e 2. d b 5. b 6. b 7. e 8. c Free Response 9) We wnt to test Ho: μ=, H: μ where μ = men weight loss 9b) SRS The subjects were probbly not rndom smple, hopefully they re representtive of lrger popultion Normlity smple size is lrge enough to ssume normlity (n>3) Independent The popultion is esily greter thn 1 * 47 9c) Using Tble C nd df=5, we cn see tht the p-vlue is less thn.5 (off the chrt) 9d) This mens tht over the 6 months, there ws significnt men weight loss for the subjects. The results do not pper to hve hppened by chnce. 1) Popultion of interest is ll bgs of plin M&Ms. We wnt to test Ho: p=.2, H: p.2 1b) SRS The bg must be thought of s rndom smple of ll plin M&Ms Normlity np =12.2 nd n(1-p )=48.8 both re t lest 1 Independent The popultion of ll plin M&Ms is esily t lest 61 1c) Test sttistic is z = ( ) / root( (.2)* (.8) / 61) = 2.18 nd p-vlue =.292 1d) There is sufficient evidence to reject Ho md conclude tht the true percentge of yellow M&M s is not 2% 1e) The 9% confidence intervl should be * root( (.311)(.689)/61) ) = (.214,.48) Chpter 12 5 Test 12A