Test 2_Key

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University of South Florida *

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3024

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Statistics

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Apr 3, 2024

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Name (Print): [ £Y Student U #: Signature: o STA 3024 — SECOND TEST — Spring 2023 — Rimbey Instructions: Print your name above and provide your signature and U number. This test consists of 11 problems worth the points indicated by the problem and is worth a total of 90 points. Please make sure you have all 11 problems. Show all your work on these pages. Do not use scrap paper. Only approved scientific calculators are allowed on this test; all others will be taken away and incur a penalty. Calculators can NOT be shared. Cell phones must be turned off and kept out of sight. Problem Score T -

1. (10 points) A physician wants to determine whether an experimental medication affects an individual’s heart rate. She randomly selects 10 patients and measures the heart rate of each. The subjects then take the medication and have their heart rates measured after one hour. The results are shown in the table below. (a) Fill in the data for the last four columns. Absolute Patient | Before | After | Difference Value Rank | Signed Rank I 7 | 75 -5 3 £.5 ~4.5 2 78 75 5 3 5.4 5. 3 75 75 o © - - 4 68 63 g S 1 g 5 80 76 4 4 G s 6 70 68 = L 3 3 7 66 66 O 0 - - 8 7 74 -2 (= 3 -3 9 75 76 ~ | { ' — | 10 74 72 "z - 5 > (b) What is the value of w_ ? Show how you are determining your answer. 5«&«\ o’&\ ~ ronks= -’S.g-s,.\ =-‘fi.§ + (‘&,.nks L5485 F+D3+3 = Z\Qg wsz M(\—QS\ )\ZL-SO :

2. (9 points) In a study testing the effects of an herbal supplement on blood pressure in men, 9 randomly selected men were given the supplement for 12 weeks. The table below shows the measurements for each subject’s diastolic blood pressure taken before and after the 12-week treatment period. Use the Paired-Sample Sign Test to determine if you can reject the claim that there was no reduction in diastolic blood pressure. Use a =0.025. + = o+ A A 4 - * Patient 1 2 3 4 5 6 7 8 9 Before treatment | 123 | 109 | 112 | 102 | 98 | 114 119 X2 | 110 After treatment 124 | 97 | 113 | 105 | 99 119 114 112 121 (a) What are H, and H, and which is the claim? (b) What is the critical value and what is the rejection region? Why? (c) What is the value of the standardized test statistic? Show how you are determining your answer. CO\,\ He 9106"@'(*& M W ;,&QQ MW(&A\MX Ll" " QMW (D) There ot fid«/xo CMJMW“Z‘”T\>

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3. (4 points) Write the generic null and alternative hypotheses for the two Wilcoxon tests. LL //C\L—EUL)O/YVT\AIQ‘J«M RM)(-&L-L S an—e : &&5‘(7. d \)( 0°~o Ao LEJ)-C. 4. (9 points) A national price-monitoring organization claims that the median price of used cars sold in the United States is $29,500. In a random sample of 85 used cars sold in the U.S., 9 sold for $29,500; 45 sold for less than $29,500; and the rest sold for more than $29,500. At a =0.025, can you support the organization’s claim? (a) What are H, and H, and which is the claim? (b) What are the rejection regions? Why? (c) What is the value of the standardized test statistic (to two decimal places)? Show how you are determining your answer. (o3 W+ madian=2a500 (cloun) W medion # 24500 (L) Furm Tkl & o dh o =025 »t'u)o—-bduz%o’-‘?_-?,‘l K”YK‘@ e E«— 2.4 &vz,zﬂ (¢) & Ll 24 S00= 48 O ak 294,500 = 9 A Jewe 24500 = §5- 46— =51 x = ma (3 4 S)= 3| L;S\—r,g)’,g(?(Q\ _T 49 '\/976/1

5. (9 points) A personnel director in a particular state claims that the mean annual income is greater in one of the state’s counties (County A) than it is in another county (County B). In County A, a random sample of 6 residents has a mean annual income of $41,900 and a standard deviation of $8800. In County B, a random sample of 8 residents has a mean annual income of $39,200 and a standard deviation of $5300. Assume the population variances are nof equal. Also assume the samples are random and independent, and the populations are normally distributed. (a) If Table 5 were used to determine the rejection region(s), what value would you use for d.f. ? Show how you are determining your answer. (b) What is the value of the test statistic (to three decimal places)? Show your work. (c) If StatCrunch is used on this problem, will it produce the same answers as those obtained using the Formula Sheet and Table 5? Why or why not? CG"\) o\& = MmN C(\‘.—\ )“L-\\ T AN (g)—}\ :_@ Gy € = 2 TF) T A =4051,q0L34¢ _ (41,300 -39, 200y~ 0 =| O, (t’b Qogl, 0848 (/C)l\;") SMMWWJ%MA Sl S:of OQQ_ MM MV\RM(}X

6. (6 points) The salaries (in thousands of dollars) of a sample of teachers from State A and a sample of teachers from State B are shown in the table below. If the Wilcoxon Rank Sum Test were used on this data, what would be the value of R ? Explain your answer. Ordered Salaries Sample Rank 30 B 1 35 A 2 - 40 B 3 45 A 4 - 50 B 5 55 B 6 60 A 7 ~ 65 A 8 ~ 70 B 9 75 B 10 80 A 11 - 85 B 12 Mhew bae § A's L FD5 56 =5 4 n=F 2 Vo .VL(, St -vL& Aa/wQQS &\. N, (a.e.(‘\\) S R= IS S

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7. (12 points) A travel consultant claims that the standard deviation in hotel room rates is lower in Tampa than in Orlando. A sample of 8 hotel room rates in Tampa has a standard deviation of $54 and a sample of 9 hotel room rates in Orlando has a standard deviation of $30. At a =0.05, can you reject the travel consultant’s claim? (a) Write mathematical statements of A, and H,. Which is the claim? (b) What is the rejection region? Why? (c) What is the value of the standardized test statistic (to two decimal places)? Show how you are determining your answer. (d) Should you reject or fail to reject the null hypothesis? Why? (a gfi/c \:/r&-v\fO\. Z. 1= O/‘\«Mo(a (“Wfot,,&:{AO) /ﬂ\w l—\—o:o“z_o"z_@_ ! B 0'1((;',(0%3 )/(Lls o &Jb—M\J)w Qg_:t‘:SfT«cueJ Mlfiyfi‘ —Wi( Ay d§.y=n-t=2 L AL =0, -1 =4 From T3 £, 2 5,40 = e [F>3.60) _sE st c =2 _ 94- © F 3,k 50"' (P Snce 3.24¢ 3.0, {xild & et 18

7. (12 points) A travel consultant claims that the standard deviation in hotel room rates is lower in Tampa than in Orlando. A sample of 8 hotel room rates in Tampa has a standard deviation of $54 and a sample of 9 hotel room rates in Orlando has a standard deviation of $30. At & =0.05, can you reject the travel consultant’s claim? (a) Write mathematical statements of H, and H,. Which is the claim? (b) What is the rejection region? Why? (c) What is the value of the standardized test statistic (to two decimal places)? Show how you are determining your answer. (d) Should you reject or fail to reject the null hypothesis? Why? (ofe - e led \ s 3 s, 30" = (C\ F: - 52.. = SqL = O' C) ‘4% (D A=a-1=3,dL =7 To apx £ ~FL AL - FnT. NN SRS ?\Aib,fi = 350 (L Tude ) a1 _ ) { g\e"" Fy = 3'1;:5 = LO% = /Rﬂ R F(O,Zfa (A e 3095280 = Q;&__@%&H@

8. (3 points) (multiple choice) d-u, Sq Az (a) The standard deviation of the differences between the paired data entries in the dependent samples. (b) The standard deviation of the difference between the means of the paired data entries in the dependent samples. (c) The standard deviation of the data entries in the combined sample. In the formula ¢ = , what does the symbol s, represent? (d) The standard deviation of the differences between each data entry and the mean of the data entries. Answer: e 9. (4 points) Fill in the blanks. For all F-distributions, the mean value of F is approximately equalto | . The total area under each F-distribution curve is equal to \

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10. (12 points) Test the claim u, =0 about the mean of the differences for a population of paired data at the level of significance a =0.10. Assume the following samples are random and dependent, and the populations are normally distributed. Sample A 2.5 6.3 2.4 8.2 Sample B 12.1 2.1 7.2 10.6 '"Q:»Q L‘.?.. “'4:X "’Z..L{ Note: 5, =5.742 (You do not need to derive this.) (a) What are the null and alternative hypotheses? Which is the claim? (b) Determine the rejection region(s). Explain your answer. (c) Determine the standardized test statistic (to three decimal places). Show your work. (d) Should you reject or fail to reject the null hypothesis? Why? (& Ro: My =0 (O(M“\ S “A.: Nkoqé O (p) Var Tade S Wt (ko ~toilad | ond 4.8 =U-1=3=> ¢ =2 343 = 2R Lfi<" 2353 e>z,3?§) () L= _E\_:'_J.\_‘\-é- ,)L,JC_ Z\‘:',q'c’*q'qufiﬂz‘ ‘-“'3.!4 . a2Vim L, - ‘:}_l_i_;,g. =|-1L.09% S D (AB §*‘\U-"’ 2.3 L~10%7 £ 2.353 \ we,auu.e_/“_-;i'_t — il R, 0 on o) o e

11. (12 points) A researcher claims that the distribution of the amounts that parents give their children per week for an allowance is different from the distribution shown in the pie chart on the left below. You randomly select 1500 parents and ask them how much they give their children per week for an allowance. The table on the right below shows the results. At a =0.005, test the researcher’s claim. $51 or more 3 $5 or less $21108 Survey Results 22% Response Frequency, f $5 or less 220 $6 - $10 312 ‘ $11-3820 530 $1 '3;‘;520 $21-$50 337 851 or more 101 (a) What is the rejection region? Why? (b) What are the expected frequencies? Show how you are determining your answers. (c) Calculate the value of the test statistic (to three decimal places). Show your work. (o~ Cam Tl wstls w008 E A G =k =4 D o AT =\4860 = R :[of H14.3L0) () §5 or (ass @ U o 1§ 00=)#(,—no: 229, of 1400:@) fn-20 37, ocp (500 = @) $20-50:22%, c&\ (50D ’:@) ¥4I of Mole 7—70 OS-\ 1500 = 10 | 2 (> a5 LOE- ey (Z?.o—’z,\(fi"-)r (3\2.-330) + (830-925)° 2o 330 TAS 2 2 x (35%-336) " (101-10%) 230 1 0S = 4L+ G318 A, 0420+ 14851152 ﬂ“;fiObx 0

Test 2_Key

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