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Sample Final Solution

Sample Final Solution - Sample Final Exam PSTAT 5E Fall...

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Unformatted text preview: Sample Final Exam PSTAT 5E, Fall 2011 1. A group of 24 randomly selected students have a mean score of 30.8 with a standard deviation of 4.5 on a placement test. Assume that these data come from a population that is normally distributed. What is the 90% confidence interval for the mean score, ,a, of all students taking the test? 7"- (k—I) S ('k"\ (1‘3) + V g _ ,. X... éd/b ”I" (”d/z : £0.93‘ = ['7/L/ 3053 1177/4 if. J 1 4' 304825 15‘? (7. 01.7.3) 3 1. 3‘7) 2. The table below is from an study comparing people who regularly drink wine with dinner to those who do not regularly drink wine with dinner. In the survey, each person was asked whether they drink wine with dinner and also whether they usually fall asleep within 20 minutes of going to bed. Do not drink wine Total 1-90 Drink wine Fall asleep within 20 min Fall asleep after 20 min Total 330 (a) Test whether drinking wine and falling asleep quickly are independent of one another at the a = 0.05 level . ,1 . . ”5) I WMZ, M "be 4.133114%ij HA L [Ii/#4. Ila/414°? 17M "MP/”1041‘ . IEIOxCIO a“ - '50:) =57 ’Xlr 2:6“)? ““751 (rm—m» awe?- (swat 3‘7 4' 133 4 ‘53 + 77‘ =Ll‘37 {2991;45‘...¢¢. d“) Writ, If (fl/£3173»? I.“ AME!- JL. 1.?!va (b) From this test, can we say that drinking wine will cause one 0 fall asleep faster? 3. A study was done to see how washing hands may affect chances of contracting common sicknesses like the cold or flu. A random sample of 180 individuals were selected and asked whether they regular wash their hands and whether they had recently been sick. The data is given below: Wash hands Do not wash hands Recently sick Not recently sick Total 180 (a) Of all the people who recently got sick, what proportion claim to wash their hands on a regular basis? ’Lfl VO:Q§ (b) State the hypotheses to test whether hand washing and sickness are independent and obtain the expected cell counts under the null hypothesis. (c) Calculate the chi-squared test statistic. .z ( fie)?“ . l - Z’ fl = c. L/ 3 ”L 1 X ”3661) (d) Make a conclusion at the a = 0.025 level. (You may use the rejection region or p-value method.) 34,“, 6143 > 5024) %J#‘ 4. In a study of air pollution in US cities, three variables were measured: city elevation (X), air pollution (Y), and city population (in thousands) (Z). The following statistics were gathered for the 62 cities in the study: g? = 760 s: = 1 ,800,000 s“, = —47,430 Y_= 10.7 53 = 372 s“ = —140, 750 Z = 65 s3 = 7, 344 SW = 990 (a) Find the correlations my and ryz. { _ m, - HIT-I30 Y" .L..,, = : —()‘7c l .I'm. at, f—"‘—--—-—-—-1)0<‘[email protected]fi x 371 [<5 81y 9 Q0 f = ~_~ -——--—-"—""—' ': 3E] .131‘691' [7390/ x 371‘ Q‘s—(7‘7 (b) Is city population or city elevation a better predictor of pollution? Why? am ”Madam {gm map/V37] (c) Is there a positive or negative correlation between X and Z? How can you tell? (There are numerous correct reasons, even without explicitly calculating TM.) ”7435;.“ SK; 40 at, M X?) Vt (rxyw) M WZ ,éufizwf (agilom 04924713.. [ray )0) €67 C44. 95W ZWCW 5. In a study about college student study habits, the following information is gathered on three variables: number of hours per week spend studying (X), number of extracurricular associations belonged to ( Y), and college GPA (Z): )‘g = 12.4 2(2; — as)2 = 144 Xxx.- — i)(y,~ — g) = —8.7 2(a) — i)(z.- — z) = 13.2 3’ = 26 my — 1.7)2 = 7-35 2(a- — 37x2. — 2) = —0-45 Z = 2.76 2(z — 2)2 = 3.0375 Determine which of the following are true and false: (a) T 'Q umber of extracurricular activities (Y) is a better estimator of college GPA (Z) than is hour spent studying (X). r” . L315; _ _0 J73< (wavy) ” 0675' r (3.1 ‘ ‘ XL _"’ — 0.63/ [I HH ( 3.0370 ([email protected] F: Students in three associations tend to study about 1.18 hours fewer per week than those ' two associations. (Hint: Regress X on Y) b? Z(x,-~‘>‘<)(y,._<-,) _ 537.7 Z{\/’.__(7)7- 735, : l— I [(6 (c) T or i A reasonable GPA estimate for someone who studies 30 hours per week is 4.38. (Hint: The r greasion equation from the above data is 2 = 1.62 + 0.09293) ij Lififliy/fiajfik (We, Ova/.0) (d) T org-3919mm the regression equation given in (c), we can say that every extra hour of studying causes a GPA increase of 0.092. W 6. In an effort to look at the impact of pollution on beach and ocean wildlife, measurements of water contaminants (X) and variety of wildlife ( Y) were taken. Summary statistics for 52 randomly sampled locations are given below: Min Max Mean 2(wi — 502 'X 0.2 34.7 10.6 555 Y 17 89 46.2 3,685 Em — X)(Yi — Y) = —1001 (a) Find the least squares estimates and and give the estimated regression line. i) _ ~ I 00/ 4 . 5"3‘3— —‘ ”-l-ifio; J 6313 - /.<&03>< £30 : H6. 2 - (v/fiog) I0. (5 3 6C. 3 (b) Say one sample has X = 12.3 and Y = 40. What is the residual for this subject? 4 U: 693 #3030155): #3. 12m was/Me vv 9‘.— wa-q-slnm =-3‘/23/ (0) Would it be reasonable to predict Y for a new observation with X = 75? ((1) Find the 95% confidence interval for My at X = 10.6. (Use sylw = 7.5) 4 n4) —*—.——m - , it to; 6w l5 ' #6225 1.07 . l r. lac—rem)“ (L/H. H) H€14> Henley/(7s) #1 m (e) Find the 95% prediction interval for Y at X = 10.6. (Use Sylm = 7.5) A (m) r"*_‘_—TD 96, <- //+é+ “we J 0% 7/x 1: (‘4‘ -;)L 416.23 2.0001 C7.<)~l l + 5’; *0 Hé-Zi 152/ (30/701) GAL/I) 7. A friend tells you that at most 60% of UCSB students are registered as Democrats. You don’t believe him, so you decide to do a hypothesis test. You sample 80 students and find that 50 are registered as Democrats. (a) State your hypotheses for this test ) 4‘ Ho, - p“ 0, 6 HA: P >0. 6 (b) Check the necessary assumptions for this test (MM S’WV’ # I d H W [75!" (0) Calculate the test statistic _ {in {’c- 0.628'~0_é 3L {$071)} : a6 (an) : 0* C/S'é V\ 870 (d) Compute the p-value ,/""_—‘ H _\m/€Mb : “J v 43/ %fl _ F 03227 0 aficé (e) Make a conclusion at an a _= 0.05 level. _%MMM anaemia/61% a 7.1%; 7%.“, (02:. ...
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