STP 226 EXAMPLE EXAM #1 Istructor: Hoor Statemet: I have either give or received iformatio regardig this exam, ad I will ot do so util all exams have bee graded ad retured. PRINTED NAME: Siged Date: DIRECTIONS: This is a closed book examiatio. You may use a graphig calculator ad a idex card with had writte otes, o completely solved problems are allowed. Formulas are o the reverse side of the frot page of the test. There are 11 problems. Three extra credit poits are icluded. Provide complete ad well-orgaized aswers. Show your work! Relax ad good luck!
Questio#1 (8 poits) The followig are legths ( i iches) of radom sample of 7 rattlesakes: 15, 7, 10, 13, 20, 8, 25 Compute sample mea ad sample stadard deviatio for this data set by had usig oly basic calculator fuctios. Use defiitio, ot a computatioal formula. Show all work! Roud your aswer to 2 decimal places, use proper otatio ad give uits. ANSWER: Questio#2 (4 poits)give mode for the followig data set, if there is o mode, state it. The followig table gives umber of babies bor o each day of the week i 2002 (i thousads). What day (if ay) is the mode? Day Births (i thousads) Moday 11.5 Tuesday 12.8 Wedesday 12 Thursday 12.4 Friday 12.4 Saturday 8.6 Suday 7.5 Mode: Questio#3 (4 poits) Data from a medical study cotais values from may variables for each of the people who were subjects of the study. List all qualitative variables. a. Geder (Male, Female) b. Age (years) c. Race (Asia, black, white, other) d. Smoker (yes, o) e. Systolic blood pressure (millimeters of mercury) f. Family size (umber of people i the family, icludig self) ANSWER:
For Questios #4 ad #5 use a frequecy histogram is give below for the weights of a sample of college studets. Frequecy Weight i pouds Questio#4 (4 poits)assumig there are 290 studets i the data, estimate % of studets with weight betwee 120 ad 130 pouds ANSWER: Questio#5 (4 poits)fill i the blak i the followig statemet, usig possible aswers give below: Distributio shape of the above data ca be best described as A) right skewed B) J shaped C) uiform D) bimodal E) Left skewed Questio#6 (4 poits) A survey of affluet Arizoa residets (those with aual icomes of $75,000 or more) idicated that 57% would rather have more time tha more moey. Assume that survey used a sufficietly large simple radom sample. Would it be reasoable to geeralize from the sample to say that 57% of all Arizoa residets would rather have more time tha more moey? Explai briefly why or why ot.
Use followig iformatio for Questios #7 ad #8 The followig data o x=score o a measure of test axiety ad y= math exam score was collected for a radom sample of 9 studets. Higher values of x idicate higher levels of axiety. x 23 14 5 1 17 10 20 15 21 y 43 59 66 75 50 60 46 53 51 Questio#7 (10 pts) Obtai the equatio of the least squares regressio lie for the data, use x as explaatory variable ad y as a respose variable. You may use your calculator. Roud aswer to 2 decimal places. ANSWER: Questio#8 (5 poits) What is the percetage of total variatio i y values that is explaied by the regressio lie you computed i Questio #7? ANSWER: Use followig iformatio i Questios #9 ad #10 Box plots give below summarize the weight loss i pouds for two types of diet programs : Program A (top plot) ad Program B (bottom plot). A B 8 10 12 14 16 18 20 22 24 Questio#9 (5 poits)give rough values of 5 umbers summary Program A data set (top plot): Mi= Q1= Med= Q3= Max= Questio#10 (4 poits)decide if the followig statemets are true or false: A) Program A has less variability i the middle 50% of the data tha program B True False B) Program B has smaller rage tha Program A True False C) Program B has a symmetric distributio True False D)Media weight loss is smaller for program B tha for program A True False
Questio#11(6 poits) Cosider the stem-ad-leaf diagram give below. Data represets age of oset of diabetes for a radom sample of 28 Americas. The quartiles of this distributio are: Q1= 49 Q2=55.5 Q3=63. Compute Iterquartile Rage IQR ad use it to check if there are ay potetial outliers i these data. Show all work, list outliers, if there are o outliers, state it. 1 3 1 2 stems: tes 2 3 leaves: oes 3 5 4 1 3 4 7 8 8 5 0 1 1 3 4 5 5 5 6 7 8 9 6 0 2 3 3 4 6 5 6 7 7 2 7 8 OUTLIERS: Use followig data for Questios #12 ad #13 The followig table summarizes weekly study time i hours of selected radom sample of 150 studets i a Calculus class: Study Time (hours) Relative Frequecy 1 0.10 2 0.20 3 0.34 4 0.22 5 6 0.02 Questio#12 ( 3 pts) Compute missig relative frequecy i the table ad give the umber of studets that had more tha 4 hours of study time? MISSING RELATIVE FREQUENCY: Number of Studets : Questio#13 ( 6 pts) Compute the mea ad media study time for these studets. MEAN: MEDIAN:
Use followig iformatio for Questios #14-#19 Professor plots the readig scores of 60 fifth-grade studets agaist their IQ scores ad he observes a liear tred. The IQ scores i the collected data are betwee 80 ad 127 poits. The least squares regressio equatio for predictig a readig score (y) from IQ score(x) is give below: ŷ= 33.4+0.882x I each statemet fill i the blak, use possible aswers give below each statemet. (3 poits each) Questio#14 For each poit icrease i IQ score (x) he predicted readig score y poits A) icreases by 0.822 B) icreases by 0.882 C) decreases by 33.4 D) icreases by 33.4 Questio#15 The predicted readig score for a studet with IQ=105 is A) 156.46 B) 59.21 C) 72.482 D) oe of these Questio#16 Predictig readig score for studet with IQ=160 will be called ad may ot give reasoable results. A) correlatio B) itegratio C) extrapolatio D) regressio Questio#17 The correlatio coefficiet for these data will be A) positive B) egative C) zero D) ot eough iformatio Questio#18 Y-itercept of the equatio gives predicted readig score for IQ= A) 10 B) -1 C) 0 D) oe of these Questio#19 Least squares regressio lie has smallest possible A) predictios B) correlatio coefficiet C) slope D) sum of squared errors I Questios #20-#25 decide if each statemets is true or false (3 poits each)
Questio #20 Suppose test scores i a large sample of Mat 117 studets have mea of 70 poits ad stadard deviatio of 5 poits. Accordig to the Three - Stadard Deviatios - Rule we ca say that very few studets had fial exam scores below 55 poits or above 85 poits. True False Questio #21 Mea ad stadard deviatio of ages for populatio of ABC Uiversity studets this are 26 ad 4 respectively. A z-score for oe radomly selected studet is z = - 1.5. This studet is 20 years old. True False Questio #22 Suppose we collected two samples of studets ad we measured their height i iches. The sample that has more variability will have smaller sample stadard deviatio. True False Questio #23 If the distributio of a sample data set is left skewed, the mea of that data will be larger tha the media. True False Questio #24 I the Least square regressio aalysis if the regressio equatio is y=2.34 1.75x ad the coefficiet of determiatio is r 2 = 0.36, the we ca determie the correlatio coefficiet to be r = 0.6. True False Questio #25 A correlatio coefficiet of 0.62 suggests a stroger liear relatioship tha correlatio coefficiet of - 0.84. True False
FORMULAS Sample statistics Sample mea: x x= i, Sample stadard deviatio (defiitio) Computatioal formula x s = i x 2 x 2 i x i 2 1 s = 1 Rage=Max-Mi Iterquartile Rage IQR= Q 3 -Q 1, Lower Limit LL=Q1-1.5(IQR), Upper Limit UL=Q3+1.5(IQR) Populatio mea: = x i N or = x i 2 Populatio parameters: Populatio stadard deviatio: = x i 2 N 2 Stadard score or z-score z = x μ σ Regressio ad Correlatio N 1 x i x y i y Liear correlatio of X ad Y 1 r = = s x s y S xy S xx S yy Least-Squares Regressio equatio y =b 0 b 1 x, b 1 = S xy S xx, b 0 =y b 1 x Coefficiet of determiatio: r 2 = SSR SSE =1 SST SST SST = y i y 2 =S yy SSR= y i y 2 = S 2 xy S xx SSE= y i y i 2 =S yy S 2 xy S xx Regressio Idetity: SST=SSR+SSE S xx = x i 2 x i 2 KEY, S yy = y i 2 y i 2, S xy = x i y i x i y i
1) 6.58 iches 2) Tuesday 3) a,c,d 4) ~24% 5) D 6) No, this sample is ot represetative of etire populatio of AZ residets. 7) ŷ=74.45 1.33x 8) 94.2% 9) roughly: 16, 16.5, 19, 22, 23 10) T,F,F,T 11) IQR=14, outlier:13 12) 0.12, 21 studets 13) mea=3.12, Media=3 14) B 15) B 16) C 17) A 18) C 19) D 20) T 21) T 22) F 23) F 24) F 25) F