AP Stats CH1 Practice Test 0809 with solutions PDF

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Chapter 1 Practice Test (0708 Actual—WITH SOLUTIONS)

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Mul t i pl eChoi c eQue s t i ons :4po i n t se a c hCORRECTI SI NBOLD 1. A researcher reports that, on average, the participants in his study lost 10.4 pounds after two months on his new diet. A friend of yours comments that she tried the diet for two months and lost no weight, so clearly the report was a fraud. Which of the following statements is correct? (a) Your friend must not have followed the diet correctly, since she did not lose weight. (b) Since your friend did not lose weight, the report must not be correct. (c) The report only gives the average. This does not imply that all participants in the study lost 10.4 pounds or even that all lost weight. Your friend’s experience does not necessarily contradict the study results. ( d )I no r d e rf o rt hes t ud yt ob ec o r r e c t , wemus tno wa d dy o urf r i e nd ’ sr e s u l t st ot ho s eoft h es t u d ya n d r e c o mp ut et hen e wa v e r a g e . ( e )Yo urf r i e ndi sa no ut l i e r .

2 .Th ef o l l o wi n gi sa no g i v eont h en umb e ro fou nc e so fa l c o ho l( o neo un c ei sa bou t30mL)c o ns ume dp e r we e ki nas a mp l eof1 50s t u d e nt s .

A study wished to classify the students as “light”, “moderate”, “heavy” and “problem” drinkers by the amount consumed per week. About what percentage of students are moderate drinkers, that is consume between 4 and 8 ounces per week? (a) 60% (b) 20% ( c )4 0% Expl a na t i o n:60 %o fs t ude nt sdr i nk8o rf e we ro z .2 0% dr i nk4o rf e we r , s o4 0% f a l li nbe t we e n. ( d)8 0 % ( e )5 0%

3. “Normal” body temperature varies by time of day. A series of readings was taken of the body temperature of a subject. The mean reading was found to be 36.5° C with a standard deviation of 0.3° C. When converted to °F, the mean and standard deviation are °F = °C(1.8) + 32). ( a) 9 7. 7 ,32 ( b) 9 7. 7 ,0. 3 0 ( c )9 7 . 7, 0 . 54Meauresofcenterareaffect e dbymul t i pl yi ngandaddi ng.Me as ur e sofs pr e adar eaffe c t e donl ybymul t i pl i c a t i o n. ( d) 9 7. 7 , 0. 9 7 ( e )9 7 . 7, 1 . 80 Chapter 1

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4. You measure the number of children, marital status and earned income of an SRS of 1463 women. The number and type of variables you have measured is ( a )14 63 ;a l lq u a nt i t a t i v e . ( b )f o ur ;t woc a t e g or i c a la ndt woq ua nt i t a t i v e . ( c )f o ur ;on ec a t e g or i c a la ndt h r e eq ua n t i t a t i v e . ( d )t h r e e ;t woc a t e g or i c a la ndon eq ua n t i t a t i v e . ( e )t hr e e ;o nec a t e g or i c ala ndt woqua nt i t a t i v e . 5. Consumers’ Union measured the gas mileage in miles per gallon of 38 1978–1979 model automobiles on a special test track. The pie chart below provides information about the country of manufacture of the model cars used by Consumers Union. Based on the pie chart, we may conclude that: ( a )J a p a ne s ec a r sg e ts i g ni fic a nt l yl o we rg a smi l e a g et ha nc a r so fo t he rc o un t r i e s .Th i si s b e c a us et h e i rs l i c eoft h ep i ei sa tt h eb o t t o m oft h ec h a r t . ( b )U. Sc a r sg e ts i g ni fic a nt l yh i gh e rg a smi l e a g et h a nc a r sf r om o t he rc ou nt r i e s . ( c )Swe d i s hc a r sg e tg a smi l e a g e st h a ta r eb e t we e nt h o s eo fJ a p a n e s ea ndU. S. c a r s . ( d )Me r c e d e s ,Au di , Po r s c h e , a n dBMW r e p r e s e n ta pp r o x i ma t e l yaq u a r t e ro ft h ec a r st e s t e d . ( e )Mo r et ha nha l foft hec ar si nt hes t udywe r ef r om t heUni t e dSt a t e s . ( No t et hel i nei nbo l da bo v e .Thec ha r ts pe a ksonl yt ot hi sv a r i abl e . )

6. The following is a histogram showing the actual frequency of the closing prices on the Ne wYo r ke x c ha n g eo fapa r t i c ul a rs t o c k .Ba s e do nt hef r e q ue nc yh i s t o gr a mf o rNe wYo r kSt oc ke x c ha n g e , t h ec l a s st ha tc o nt a i nst h e8 0t hp e r c e nt i l ei s : ( a )20 30 ( b )10 20 ( c )40 50 ( d )5 0 60 ( e )30 40

Thi si st r i c ky .Yo uha v e50v a l ue s( Thes um off r e que nc i e s=50 ) ,s oy oukno wt he4 0thv a l uef r o mt hebo t t om t h i st he8 0thpe r c e t i l e .( Re me mbe r :The8 0 pe r c e nt i l ei st ha tv a l uea torbe l o wwhi c har e8 0 %o fa l lv al ue s . ) t h h Sowhe r ei st he40 v al ue ?Ag ai n,c ount i ngf r o mt hebo t t o m,y o ufindt het 4 0 v a l uei swi t hi nt he3 0 40c l as s . Yous ho ul da l s ono t et ha tt hec l as sl abe l i ngi sho r r i bl e !I nt owha tc l as swo ul dy o upl ac eav a l ueofe x a c t l y10 , 3 V2 f ori ns t anc e ?

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8. There are three children in a room, ages three, four, and five. If a four-year-old child enters the room the ( a)me a na g ewi l ls t a yt hes a meb utt h ev a r i a nc ewi l li nc r e a s e . ( b)me a na g ewi l ls t a yt hes a mebutt hev a r i anc ewi l lde c r e a s e . ( Cal c ul a t et hi sbyha ndorc a l c ul a t o ri f uns ur e ! ) ( c ) me a na g ea ndv a r i a n c ewi l ls t a yt hes a me . ( d)me a na g ea n dv a r i a nc ewi l li nc r e a s e . ( e ) me a na g ea ndv a r i a n c ewi l lde c r e a s e .

9 .

Wh i c hoft h ef o l l o wi n gi sl i k e l yt oh a v eame a nt ha ti ss ma l l e rt h a nt heme d i a n ? (a) The salaries of all National Football League players. (b) The scores of students (out of 100 points) on a very easy exam in which most get nearly perfect scores but a few do very poorly. Left skewed distribution, so mean is less than median. ( c ) Th epr i c e so fho me si nal a r g ec i t y . ( d)Th es c o r e so fs t u d e nt s( o uto f10 0p oi n t s )o nav e r yd i ffic ul te x a mi nwh i c hmo s tg e tp oo rs c o r e sb uta f e wdov e r ywe l l . ( e ) No neoft h ea bo v e .

10.

The weights of the male and female students in a class are summarized in the following boxplots:

Wh i c hoft h ef o l l o wi n gi sNOTc o r r e c t ? (a) About 50% of the male students have weights between 150 and 185 pounds. ( b )Ab ou t2 5% o ff e ma l es t ud e nt sh a v ewe i gh t smo r et h a n13 0p ou nd s . ( c )Th eme di a nwe i gh to fma l es t u de n t si sa bo ut16 2p ou nd s . ( d )Theme a nwe i g htoff e ma l es t ud e nt si sa bo ut1 20po un dsb e c a us eofs y mme t r y . ( e )Thema l es t ude nt sha v el e s sv ar i abi l i t yt hant hef e ma l es t ude nt s . ( Ma l e sha v egr e a t e rI QRorRa ng e , whi c har et heme a s ur e sofv a r i a bi l i t yhe r e , s ot hi si saf al s es t a t e me nt )

1 1. Wh e nt e s t i n gwa t e rf o rc he mi c a li mp u r i t i e s ,r e s u l t sa r eo f t e nr e p or t e da sbd l , t h a ti s ,be l o wd e t e c t i onl i mi t . Th ef o l l o wi n ga r et h eme a s ur e me n t soft hea mo u ntofl e a di nas e r i e so fwa t e rs a mpl e st a k e nf r om i n ne r c i t yho us e h ol d s( ppm) . 5, 7, 12, bdl, 10, 8, bdl, 20, 6

Wh i c hoft h ef o l l o wi n gi sc o r r e c t ? ( a )Th eme a nl e a dl e v e li nt hewa t e ri sa b ou t10pp m. ( b )Th eme a nl e a dl e v e li nt hewa t e ri sa bo ut8p pm. ( c )Theme di anl e a dl e v e li nt hewa t e ri s7ppm.( bdl , bdl ,5 , 6, 7, 8 ,10 , 12 , 20 Me di ani s7 ) ( d )Theme d i a nl e a dl e v e li nt hewa t e ri s8p pm. ( e )Ne i t he rt h eme a nno rt h eme di a nc a nb ec ompu t e dbe c a u s es omev a l u e sa r eun kno wn .

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Part 2: Free Response Communicate your thinking clearly and completely. 11. The test grades for a certain class were entered into a Minitab worksheet, and then “Descriptive Statistics” were requested. The results were: MTB > Describe 'Grades'.

Grades

N 28

MEAN 74.71

MEDIAN 76.00

TRMEAN 75.50

Grades

MIN 35.00

MAX 94.00

Q1 68.00

Q3 84.00

STDEV 12.61

SEMEAN 2.38

You happened to see, on a scrap of paper, that the lowest grades were 35, 57, 59, 60, . . . but you don’t know what the other individual grades are. Nevertheless, a knowledgeable user of statistics can tell a lot about the dataset simply by studying the set of descriptive statistics above.

modi fie dboxplotforthesedata.SeePage46inyourbook!

( a )( 5po i nt s )Con s t r u c ta

3 5

5 7

68

76

84

94

(b) (10 points)Write a brief description (prose….sentences…) of what the results tell you about the distribution of grades. Be sure to address (at least!) the following:  the general shape of the distribution  unusual features, including possible outliers  the middle 50% of the data  any significance in the difference between the mean and the median The distribution of test grades is approximately symmetric, but there is a significant outlier at 35. Because of the outlier, the preferred measures of center and spread are the Median of 76 and the Interquartile Range of 16. Note that the mean is 74.71—quite close to the median, suggesting that the distribution is not severely skewed despite the outlier. Assuming these scores are percentages, the maximum score of 94 suggests the test was quite challenging even for excellent students, and the median of 76 tells us that more than half of all students had a C or worse—assuming there are some scores between 76 and 79. Level of learning is moderate at best, assuming the test was appropriately constructed.

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1 2. Ha l l uxa b du c t ov a l g us( c a l li tHAV)i sad e f o r ma t i onoft heb i gt o et ha ti sn o tc ommoni ny ou t ha ndof t e n r e q u i r e ss ur g e r y .Do c t or su s e dXr a y st ome a s u r et hea n g l e( i nd e g r e e s )ofd e f o r mi t yi n3 8c o n s e c u t i v e p a t i e n t sun de rt hea g eof2 1whoc a met oame di c a lc e nt e rf o rs ur g e r yt oc o r r e c tHAV.Thea n g l ei sa me a s u r eoft h es e r i ou s ne s soft h ed e f o r mi t y .He r ea r et heda t a . 28 32 25 34 38 26 25 18 30 26 28 13 20 21 17 16 21 23 14 32 25 21 22 20 18 26 16 30 30 20 50 25 26 28 31 38 32 21

a )( 6p oi n t s )Co n s t r uc tamo di fie dbo x pl o t .( Don’ tf o r g e tLa be l s , Val ue sa ndSc a l e .Idi dn’ tdot he m he r ebe c a us ei t ’ st o ug ht odoe l e c t r oni c a l l y . )

b )( 5p oi n t s )Co ns t r uc tahi s t o gr a mu s i n ga pp r o pr i a t ec l a s s e swho s ewi dt hi sfiv e .Bes u r et ol a be ly o ur c l a s s e sun a mb i gu ou s l y .Th el o we n do fy o url e f t mos tc l a s ss ho ul de q ua l1 0.

He r eIdr op pe di nas c r e e ns ho tf r o mt h ec al c ul a t or .Y ou s h ou l dl ab e le a c hc l a s sc l e ar l y !

c )( 5p oi n t s )Wh a tme a s u r e sofc e nt e ra n ds p r e a da r emo s ta pp r o pr i a t ehe r e ?__Me di a na ndI QR_ _ Wh y ?Be c au s et h epr e s e nc eo ft heo ut l i e rwo ul dr ai s et heme a na nds t a nda r dd e v i a t i ona bo v ewh at wou l dbeat r uec h ar ac t e r i z a t i onoft h edat a.

d )Ar et h e r ea n yo ut l i e r s ?( 2p oi n t s )_ __Ye s , 50 __ __ _Pr o v eord i s pr o v ey o urc l a i mb yu s i n gs ho wi n g a pp r op r i a t ec a l c ul a t i on s . Th ea n g l eb e l o wwhi c hav a l uewo ul dbec on s i de r e da nou t l i e ri s : _ __ 5de gr e e s _ ___ __ __ __ __ ( 4p t s . ) Q1–1. 5 ( Q3Q1)=2 01 5=5 Th ea n g l ea bo v ewh i c hav a l uewo u l db ec on s i d e r e da no ut l i e ri s : _ __ _45de gr e e s __ ___ __ __( 4p t s . ) Q3+1 . 5( Q3Q1)=3 0+1 5=4 5 Chapter 1

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