# SampHe Exaxmixnati*rs Six - La Jolla High School

SampHe Exaxmixnati*rs Six - La Jolla High School

SampHe Exaxmixnati*rs Six - La Jolla High School

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<strong>SampHe</strong> <strong>Exaxmixnati*rs</strong> <strong>Six</strong><br />

Section I<br />

lirne-l hour and 30 miuutes<br />

Questions 1*40<br />

Percent of total grade-S0<br />

Dfrections: The quesiions or incompiete statements that foliou,are each followed by five<br />

suggested answers or eompletions. Choose the response that best ansu,ers the question or<br />

cornpleies the statement.<br />

l. A random sample of 100 people '.^,,as asked to state his or her gender and favorite ice<br />

cream flavor. The results appear in the table belou,.<br />

Male 10<br />

Female<br />

Vanilla Chocolate Strawberry<br />

aA<br />

LA t2<br />

ao<br />

LO 16 10<br />

A chi-square test is used to test the null hypothesis that gender and preferred ice cream<br />

flavor are independent. Which of the following statements is correct?<br />

(A) Do not reject Ho at the 0.05 significance level.<br />

(B) Do not reject Ho at the 0.01 significance level.<br />

(C) Reject Ho at the 0.01 significance level.<br />

(D) Reject Ho at the 0.005 significance level.<br />

(E) Reject Ho at the 0.001 significance level.<br />

2. If a null hypothesis that is actualll, false is not rejected, we have<br />

(A) made a type I error<br />

(B) made a type II error<br />

(C) made neither a Type I nor Type II error<br />

(D) obtained a sample that is definitely biased<br />

(E) chosen a null hypothesis that cannot be tested<br />

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Answer<br />

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II<br />

ll

Section I Sample Exarninatiom <strong>Six</strong><br />

3. T'he probability that a child will have a problem with alcohoi is 0.75 if-at least one of<br />

tl-re parents is an alcoholic and 0.05 if neither parent is an aicoholic. in a recent study<br />

of a large number of children , SYo of the children involved had at least one parent who<br />

is an alcoholic. If a chiid in ilris study has an alcohol-related problem, what is the<br />

probability that at least one of the parents of the child is an alcohoiic?<br />

(A) 0.0375<br />

(B) 0.047s<br />

(.c) 0.4412<br />

(D) 0.78es<br />

(E) 0.8000<br />

4. The November 2000 Presidential election had George W. Bush and Albert Gore as the<br />

2 major candidates. Suppose thatZl3 of the people in the city supported Bush but 5/9<br />

of the people in the suburbs supported Gore. 60% of the people live in the city while<br />

40Yo of the people live in the suburbs. If you select a random Bush supporter, what is<br />

the probability that the person lives in the city?<br />

(A) 1e.8%<br />

(B) 30.8%<br />

(c) 34.6%<br />

(D) 66.7%<br />

(D 69.2%<br />

r3r<br />

Answer<br />

Answer<br />

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1?t Sample Exax'ninaticn <strong>Six</strong> Seetion I<br />

5. Consider the folloq,ing test scores:<br />

Class A: 65,72,73,73,74, 82, 9l Class B: 60.65.79,81,85,86, 86<br />

Which of the following is a true statement?<br />

(A) Class A has the greater range, while Class B has the greater standard deviation.<br />

(B) Class ts has the greater range, ra'hile Class A has the greater standard deviation.<br />

(C) Tlie ranges and standarC deviations are the same for both classes.<br />

(D) The ranges are the same, but Class A has the higher standard deviation.<br />

(E) The ranges are the safite, but Class B has the higher standard deviation.<br />

6. The verbal scores of incoming freshmen at a large university are approximately<br />

normally distributed with a mean of 550 and a standard deviation of 100. The<br />

administration wishes to give an honors English course to the top 5Yo of the freshmen.<br />

What is the minimum score that must be attained to qualify for the course?<br />

(A) s50<br />

(B) 600<br />

(c) 66s<br />

(D) 71s<br />

(E) 74s<br />

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Section I Sarnple Exarnination <strong>Six</strong><br />

7 ^ The correlation coefficient is<br />

(A) a number between -1 and +l that measures the strength and direction of the<br />

linear relationship between two variables<br />

(B) a positive nurnber that measures the goodness of fit<br />

(C) always equal to the slope of the regression line<br />

(D) never equal to zero<br />

(E) the fraction of the variation in the values of y that is explained by the leastsquares<br />

regression ofy on x<br />

8. A researcher wishes to examine the relationship between years of schooling completed<br />

and the number of pregnancies in young women. Her research discovers a linear<br />

relationship, and a least squares fit of her data results in the model<br />

v=6.4-0,12x<br />

where x is the number of years completed in school andy is the number of pregnancies.<br />

What is the estimated change in the number of pregnancies that corresponds to the<br />

completion of an additional 10 years of school?<br />

(A) a decrease of 5.2<br />

(B) an increase of 7 .6<br />

(C) a decrease of 7 .6<br />

(D) an increase of 1.2<br />

(E) a decrease of 1.2<br />

r33<br />

Answer<br />

Answer<br />

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134 Sarnple Exarnination <strong>Six</strong> Section E<br />

9. What is the effect on the correlation betr.r,een trvo variables ( x, t,) if each r-value is cui<br />

in half and 0.04 is subtracted from each v-value?<br />

(A) 'rhe<br />

(B) The<br />

(C) Ihe<br />

(D) The<br />

(E) The<br />

colrelation is cut in half.<br />

correlation is decreased b"v 0.04.<br />

correlation is decreased by 0.0016.<br />

correlation is unchanged.<br />

correlation is doubled.<br />

10. A major tire manufacturer claims that his shock absorbers last for 5,000 miles. A<br />

consumer watchdog group claims ftat the actual mileage is lower. If 7: represents the<br />

true average life of the shock absorbers, rvhich of the follou'ing are the appropriate null<br />

and alternative hvpotheses?<br />

(A) Ho:l= 5000<br />

(B) Ho:p< 5000<br />

(C) Ho:tr7= 5000<br />

(D) Ho:p> 5000<br />

(E) Ho:,U= 5000<br />

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H":1t< 5000<br />

Ho /t+5000<br />

Hu: trt+5000<br />

H": trt+5000<br />

Hu: trt> 5000<br />

Answer<br />

Answer

Section I Sampie Examination <strong>Six</strong> 135<br />

ll. Which of the following are true statements?<br />

I. A census aims to obtain information about an entire population by studying a<br />

smail sample of the population.<br />

il. Sample surveys are experiments.<br />

IIL A treatment is imposed in an observational study.<br />

(A) I only<br />

(B) II only<br />

(C) Itl only<br />

(D) If and III<br />

(E) None of the above<br />

Answer<br />

12. Aresearcher plans a study to examine the attitudes of residents of Califomia towards a<br />

proposal in Congress to declare English to be the official language of the state. He<br />

obtains a random sample of 50 residents of one community in California and all agree<br />

to participate. Which of the following statements is true?<br />

(A) This is a poorly designed survey because it is a voluntary response sample.<br />

(B) The design of the study may be biased because the sample may not represent the<br />

population of interest.<br />

(C) It is a well-designed survey because of the 100% response rate.<br />

(D) As long as the respondents were randomly selected, there is no bias.<br />

(E) A more accurately designed study would have included opinions on this issue<br />

from residents in other states.<br />

Answer<br />

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tJb Sarnple Examination <strong>Six</strong> Section I<br />

13" The age of {.Jnited States Fresidents at<br />

cumulative proportions graph. What is ihe<br />

(A) 2<br />

(B) 8<br />

(c) i2<br />

(D) ls<br />

(E) 2s<br />

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0)<br />

H<br />

o<br />

r)<br />

1.00<br />

.90<br />

.80<br />

.60<br />

.50<br />

.44<br />

.30<br />

')n<br />

.10<br />

their inaugurations rs<br />

approxi m ate interquarli ie<br />

39.5 11.5 49.5 54.5 59.5 64.5 69.5<br />

Age<br />

dispiayed in this<br />

rarrge (IQR)?<br />

Answer

Section I Sample Examination <strong>Six</strong> -tJ /<br />

14. In testing the design of a new tennis racket, a company randomly selected 12<br />

professional tennis players and counted the number of aces each player served when<br />

using each racket in a 2-minute period. The resurts are as follows:<br />

What is the number of degrees of freedom associated with a l-test to determine if there<br />

is a difference between the number of aces served using the 2 rackets?<br />

(A) 6<br />

(B) 10<br />

(c) l1<br />

(D) 12<br />

(E) 24<br />

Flayer Racket #1 R.acB

138 Sarnple Examination <strong>Six</strong> Section tr<br />

15. Evan and Am1, are t$,o seniors in a local high school. The grades on a Calculus final<br />

which Evan took weie approximately normally distributed with a mean of 75 and a<br />

standard deviation of 7. The grades on a Fsycholog.v final rvhich Amy took were also<br />

approximatell, nonnallS' Cistributed .,vith a mean of 85 and a standard deviation of 4.<br />

Evair scored an 89 on the Calcuius finai while Arny scored a 91 on the Psl,chology final.<br />

Relative to tl-re students in each class. u4ro did better on the final?<br />

(A) Evari<br />

(B) Amy<br />

(C) Both r,r,ere the same<br />

(D) You canaot compare a matlr course to a science course<br />

(E) There is not enough information to ansrver this question<br />

16. The distribution of lengths of boa constrictors is approximately normalll'distributed. If<br />

11.5% of these snakes are more than 147 inches long and 2.3o/o are less than 139 inches<br />

long, what are the mean and variance of tl-re lengths of boa constrictors?<br />

@) It= 142,o2= 4.72<br />

(B) p=143,o2=2.5<br />

(c) lt= 143,o2 = 6.25<br />

(D) lJ = 144,O2 = 2.5<br />

(E) p= 144,o2 = 6.25<br />

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Section I Sarnpte Exarnination <strong>Six</strong> tr39<br />

17. Whioh of the following are true statements?<br />

L The alternative hypothesis is two-sided if deviation from the null h1'pothesis<br />

is relevant in either direction.<br />

IL Hypothesis tests are designed to measure the amount of evidence that exists<br />

against the alternative hypothesis.<br />

IIi. A well pianned test of hypothesis eliminates the need for a control group in an<br />

experiment.<br />

(A) I only<br />

(B) iI only<br />

(C) III only<br />

(D) I and III only<br />

(E) I, II, and III<br />

18. Two different methods of teaching French are under consideration. In the first rnethod,<br />

a public television program is shown to the class, and a teacher spends the rest of the<br />

period revierving the concepts viewed in the program. In the second method, a textbook<br />

and traditional teaching methods are empioyed. After a period of time, an exam is<br />

administered to allthe students. The test scores of the 21 students in the first class had<br />

a standard deviation of 11.01 and the test scores of the 23 students inthe second class<br />

had a standard deviation of 17. 15. If the difference between the mean test scores of the<br />

2 classes is 9.95, is there sufficient evidence to conclude that there is a difference<br />

between the methods?<br />

(A) We cannot draw any conclusion rvithout knowing the means of the individual<br />

classes.<br />

(B) There is sufiicient evidence to conclude that there is a difference between the<br />

methodsatd=0.05<br />

(C) There is sufflcient evidence to conclude that there is a difference between the<br />

(D)<br />

(E)<br />

Answer<br />

methodsatd=0.01<br />

There is insufficient evidence at a = 0.05<br />

Since the sample sizes are different, we cannot perform any statistical analysis.<br />

Answer<br />

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140 Sarnple Examination <strong>Six</strong> Section tr<br />

19. The Central Liniit Theorem of statistics states which of the fotlowing for a sample of<br />

size n, (n > i),<br />

(A) the si,ape of the sampling distribution of sample rneans is always normal<br />

(B) the mean of the set of sample means is always less than the mean of the population<br />

(C) the standard deviatiern of the set of sample means is equal to the standard<br />

deviation of the population<br />

(D) the mean of the set cf sample means is equal to the mean of the population rvhen<br />

n is large<br />

(E) the standard deviation of the set of sarnple means is greaterthan the standard<br />

deviation of the population<br />

20. George Washington <strong>High</strong> Schooi has a distribution of grade point averages which are<br />

approximately normally distributed with a mean of 2.5 and a standard deviation of 0.5.<br />

All students q'ith a 3.5 or higher grade point average graduate with honors. According<br />

to the Empirical Rule, approximately rvhat percentage of the students will graduate<br />

nith honors?<br />

(A) 2.5%<br />

(B) 59'o<br />

(c) t3.s%<br />

(D) 16%<br />

(E\ 9s%<br />

2l. lf X is a normally distributed random variable with a mean<br />

deviation of 4, then P (14 < X < 82) is<br />

(A) 0.1e1s<br />

(B) 0.2417<br />

(c) 0.4332<br />

(D) 0.6247<br />

(E) 1.0000<br />

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Ansrver<br />

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[]<br />

of 80 and a standard<br />

Ansrver

Section I Sample Examination <strong>Six</strong><br />

22' The mean of a set of'data is 40 pounds and the standard deviation is 8 pounds. What<br />

value of an observation corresponds to a z-score of _1.25?<br />

(A) -30<br />

(B) -s0<br />

(c) 30<br />

(D) 32<br />

(E) 50<br />

23. Suppose you select a random sample of size 5 from a normal distribution with unknown<br />

mean /l and unknown variance 02. The null hypothesis Ho:/t=65 is to be tested<br />

against the alternative hypothesis Hu:H#65 atrr,= 0.05. If the resulting sample mean<br />

is 68'25 and s2 = 9, what is the value of the appropriate test statistic and the conclusion?<br />

(A) 1.96; reject Ho<br />

(B) 2. 132; reject Ho<br />

(C) 2.132; do not reject Ho<br />

(D) 2.a2; reject Ho<br />

(\ 2.a2; do not reiect Ho<br />

24. A die was rolled 24 times with the followins results:<br />

Number of dots I 2<br />

a<br />

J 4 5 6<br />

Frequency 2 8 2 J 8<br />

A goodness-of-fit chi-square test is to be used to test the null hypothesis that the die is<br />

fair. At a significance level of d =.01, the value of chi-square and the decision reached is<br />

(A) 12.5; do not reject the null hypothesis<br />

(B) 12.5; reject the null hypothesis<br />

(C) 25.0; do not reject the null hypothesis<br />

(D) 25.0; reject the null hypothesis<br />

(E) 75.5; reject the null hypothesis<br />

t4t<br />

Answer<br />

TAnswer<br />

Answer<br />

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42 Sarnple Examination <strong>Six</strong> Section E<br />

25. A study found that playing classical music increased worker productivity. Horvever, the<br />

researchers were not aware that the workers knew about the study while it rvas in<br />

progress. Since the increase in productivitl may have been due to the workers'<br />

knowledge that they were being studied, this is a potential example of<br />

(A) the control group effect<br />

(B) the effect of a treatment unit<br />

(C) a lurking variable<br />

(D) sampling effor<br />

(E) voluntary response bias<br />

26.The regression line of a set of data is y=2x+b which passes through the point (3,5).<br />

If x and y are the sample means of the x and y values, respectiveiy, then<br />

(A)<br />

(B)<br />

(c)<br />

(D)<br />

rtr)<br />

j= 2t+ 6<br />

n-.4<br />

J= zx+ I<br />

l-L^<br />

l=u<br />

y=x+o<br />

27. A straight line of the form y-- a+ bx is fitted to the 5 data points (1, 0), (0, 3), (3, 1),<br />

(2,-3), and (4,2) by the method of least squares. What is the value of 6?<br />

(A) -3<br />

(B) -2/3<br />

(c) -1lr0<br />

(D) 4/s<br />

(E) 4<br />

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Section I Sample Examination <strong>Six</strong> 143<br />

28. 'rhe average number of pushups a united states Marine does daily is<br />

standard deviation of 50. A random sample of 36 Marines is selected.<br />

probability that the sample mean is at most 320 push_ups?<br />

(A) 0.0082<br />

(B\ 0.3446<br />

(c) 0.6554<br />

(D) 0.8767<br />

(E) 0.9918<br />

300, with a<br />

What is the<br />

Anslver<br />

29' Which of the following statements regarding inference procedures for a population<br />

mean are true?<br />

JU.<br />

I' The data should be a simple random sample of size n drawn from the population.<br />

Il' When using a r-distribution, we generally assume the data are drawnfrom a<br />

population that has a normal distribution.<br />

III' We use a r-distribution rvhen the population standard deviation is unknown.<br />

(A) I only<br />

(B) II only<br />

(C) III only<br />

(D) I and III only<br />

(E) I, II, and IIi<br />

Find the standard error of the mean for a distribution where samples of size 64 are taken<br />

from a population with a mean of r14 and a standard deviation of 16.<br />

(A) 0.5<br />

(B) 2.0<br />

(c) 3.0<br />

(D) 16.0<br />

(E) 18.0<br />

rAnswer<br />

Answer<br />

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144 Sample Examination <strong>Six</strong> Section I<br />

31" When a national magazine rated a particular university as its choice for the #1 schooi<br />

in the nation, it stated the average salary of its graduates. The distribution of salaries<br />

was unimodal and skewed right. <strong>La</strong>ter it was determined that the figure stated rvas<br />

inflated due to the salary of one alumnus whose income was considered an outlier. If<br />

the outlier is removed' which of the follou'ing rvould defirtite!}'remainthe same?<br />

(A) mode<br />

(B) median<br />

(C) range<br />

(D) variance<br />

(E) standard deviation<br />

32. Which of the following is a correct statement?<br />

(A) An event that is certain not to happen has a probability of 1'0.<br />

(B) Probabilities are numbers whose values can be any number from -l to 1.<br />

(C) The total of the probabilities assigned to all outcomes in a sample space must be<br />

exactly 1.0.<br />

(D) Probabilities are always rvhole numbers.<br />

(E) If two events are dependent, then the probabiliqv that both events occur is the<br />

nroduct of their individual probabilities'<br />

33. Michael and Jeffare scheduled to take their midterrn exam in statistics. The probability<br />

that Michael will pass is 0.40 and the probability that Jeffwill pass is 0.60. If the two<br />

events are independent, which statement is correct?<br />

(A) The probability that exactly one passes is 0.0576.<br />

(B) The probability that exactly one fails is 0.52.<br />

(C) The probability that they both pass is 0.20.<br />

(D) The probability that they both pass is 1.0'<br />

(tr) The probability that they both fail is 1'0.<br />

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Section I Sample Exarnination <strong>Six</strong> l4S<br />

34. Find the value of'the appropriate test statistic for the given hypothesis test.<br />

Ho, trt = 59.2<br />

H^,1t*58.2<br />

cr = 0.01<br />

(A) -4 50<br />

(B) - 1.12s<br />

(c) -0.281<br />

(D) 1.r25<br />

(E) 4.s0<br />

x = )o,6f<br />

s = 4.80<br />

n= 16<br />

35. The graph below is constructed from data drawn<br />

distribution. Which set of frequendies could match<br />

0 < X < 2,2

146 Sarnple Examination <strong>Six</strong> Section E<br />

36. R-efer to the fbllorvins back-to-back stem-and-leaf plot:<br />

Wirich of the folloiving are true?<br />

9BB7 7 7<br />

100<br />

z<br />

4<br />

0<br />

5i<br />

222<br />

U<br />

I<br />

2 a<br />

A<br />

+<br />

i<br />

5<br />

,7<br />

G<br />

22<br />

34556<br />

11C)<br />

I lal<br />

4<br />

2s 67<br />

0<br />

I. The medians of the distributions are the same.<br />

II. The averages of the distributions are the same.<br />

III. The ranges of the distributions are the same.<br />

(A) I only<br />

(B) II only<br />

(C) IiI only<br />

(D) I and II<br />

(E) I and III<br />

37. An association wishes to design and conduct a poll to determine the proportion of<br />

Americans rvho oppose a lau, limiting the sale of handguns. If they rvish to be 98o/o<br />

confident that their sample results differ from the true population proportion by no more<br />

than 0.07, which of the following choices is the smallest sample size they should use?<br />

(A) 1s6<br />

(B) 215<br />

(c) 2s0<br />

(D) 300<br />

rE) 500<br />

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8<br />

TAnswer<br />

nAnsn er

I an<br />

t+ t Seetion ! Sarnple Examination <strong>Six</strong> 147<br />

38. A linear model was constructed for a set of bivariate data using least squares regression<br />

techniques. Given the residual plot shornn, what conclusion should be drawn?<br />

(A) A linear model was not a good fit for the data.<br />

(B) A linear model was a good fit for the data.<br />

(C) The correlation between tl-re original variables is close to 1.<br />

(D) The data was drau.n from a population that was not nomally distributed.<br />

(E) The study was poorly designed.<br />

39. A survey was conducted to determine the average age at which college seniors hope to<br />

retire. In a simple random sample of 101 seniors, 55 was the average desired retirement<br />

age. with a standard deviatior-r of 3.4 years. A 96% confidence interval for desired<br />

retirement age of all college seniors is<br />

(A) 54.30 to 55.70<br />

(B) 54.55 to 55.45<br />

(C) 54.58 to 55.42<br />

(D) 54.60 to 55.40<br />

(E) 54.63 to 55.37<br />

Answer<br />

Answer<br />

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i48 Sample Exaxnination <strong>Six</strong> Section I<br />

,t0. Which of the follo.wing examples satis| the requirements of a binomial seffing?<br />

I. A football coach is trying tc decide which of his 3 quarterbacks to start in the<br />

opening garne of the regular season. <strong>La</strong>st year's record shows that the number<br />

of passes completed b3, one of the quarterbacks improves as the season goes<br />

on. The coach is trying to determine the probability of that player completing<br />

9Aok af his passes during the flrst game.<br />

II. in fighting the West Nile \iirus. the EPA is concerned about hor.v much<br />

pesticide residue remains iir Central Park the rnorning after an aerial spraying.<br />

'fhe,v take grass cuttings from different sections of the park and measure the<br />

pesticide residue.<br />

ili" On "The Price is Right", a contestant can rvin a car in a game that involves<br />

selecting cards that contain 2-digit numbers. There are 9 cards to choose from,<br />

each with tq,o digits. The object of the game is to pickthe 2 cards that<br />

represent the first 2 digits and the last 2 digits of the price of the car. She has<br />

up to 5 chances to pick a card. Each time a card is chosen, it is removed from<br />

the game.<br />

(A) I only.<br />

(B) II only<br />

(C) III only<br />

(D) All of the above<br />

(E) None of the above<br />

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Answer

Section Itr<br />

Fart A<br />

Time-65 minutes<br />

Questions l-5<br />

Percent ofSection II srade-75<br />

Dirqclisns: Show all your work. Indicate clearly the methods you use, because you will<br />

be graded on the correctness of your method as well as on the accuracy of your results<br />

and explanations.<br />

l. The motor vehicle bureau claims that 42oh of all new cars are Sport Utility Vehicles<br />

(SUV)" Police Department sources feel that the true proportion is actually higher. To<br />

check this claim, the police department randomly sampled new car dealers and found<br />

that 95 out of 200 new cars were SUV's.<br />

(a) Is there sufficient evidence to reject the motor vehicle bureau's claim at the 0.10<br />

level of sisnificance? Show all work.<br />

(b) Find a 95oh confidence interval for the true proportion of new car owners having<br />

SUV's. Interpret this interval.<br />

L49<br />

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15fi Samp[e Exarnination <strong>Six</strong> Section Itr<br />

2. A conscientious political science major gathered the follorn'ing data froin a random<br />

sample of college fieshmen.<br />

Political Farty vs. Gender<br />

Dernocrats R.epublicans Others Totals<br />

F ernales 22 1A t7 63<br />

MaIes 16 t2 7<br />

Totals 4A 36 a^ 100<br />

Do the data provide evidence of an association between political party afhliation and<br />

gender in freshmen at the 5% level? Give appropriate statisticaljustification.<br />

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Section II Sample Examination <strong>Six</strong> 151<br />

3. The graph below displays<br />

for two Alsebra II ciasses.<br />

cum f<br />

i.00<br />

.80<br />

.60<br />

.40<br />

.24<br />

t0<br />

20<br />

(a) Find the median grade<br />

the cumulative relatrve frequencies ofthe final exam grades<br />

onehonors( )and one college Frep (- - = ).<br />

30 4A 50 60<br />

for each class.<br />

Grades<br />

(b) Find the interquartile range for each class.<br />

(c) Drarv parallel boxplots for both Algebra II classes. What conciusions can you<br />

draw from the boxnlots?<br />

70<br />

BO<br />

90<br />

r00<br />

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152 Sarnple Exarnination <strong>Six</strong> Section EI<br />

4. A game spinner has four equal sections colored red. yellow. green and blue. The poirrt<br />

values of each color are 4,3,2 and I respectively. you spirr twice.<br />

(a) v/hat is the probability that the surn of your points is an even nunrber?<br />

(b) \Vhat is the probabilify that the sun: of your points is an odd n,;mber?<br />

(c) You rvin the game if the sum of your spins is a 2 or an 8. What is the probability<br />

that you win the game?<br />

(d) If the sum of your spins is a 2 or an 8, you win $ 100. You win $50 if the sum of<br />

your spins is a 3 or a7,$24 if the sum is a 4 or a6 and $10 for a sum of 5.<br />

Compute the expected value of tl-re amount you could u'in.<br />

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Section II Sanonle Exarnination <strong>Six</strong> 153<br />

5. Ronald scores 700 on the math section of the SAT exam. l"he distribution of'SAT scores<br />

is approximately nonnal with a mean of 500 anda standard deviation of 100. Rubin<br />

takes the ACT math exam and scores 31 on the math portion. ACT scores are<br />

approximateiy normaily distributed r.r,ith a mean of 18 and a standard deviation of 6.<br />

(a) Reiative io their peers rvho aiso took the tests, who pei'fbrmed better on his test?<br />

Explair-r.<br />

(b) A certain school will only consider those students who score in the top I % in the<br />

math section. What grades would Ronald and Rubin have to receive on their<br />

respective tests to be considered for admission?<br />

(c) Between what trvo grades does 95% of the population fall for the ACT and the<br />

SAT exams?<br />

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Section II<br />

E rtg<br />

Time-25 minutes<br />

Question 6<br />

Pereent of Section I{ erade-25<br />

Directions: Show all your u,ork. Indicate cleariv the methods you use.<br />

be graded on the conectness of -1,6u. method as rveil as on the accLlracv<br />

and explanations.<br />

AP Statistics Data<br />

Student Annual Grade AP Exam Grade<br />

90 3<br />

2 92 5<br />

3 90 I<br />

4 88 A-<br />

5 67 2<br />

o 82<br />

(a) Represent this data on a scatterplot<br />

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7 90 2<br />

8 83 J<br />

9 74 +<br />

10 82<br />

,<br />

+<br />

tl 90 A a<br />

T2 t7 3<br />

IJ 90 J<br />

t4 91 5<br />

15 96 5<br />

!)<br />

tr<br />

r '')<br />

X<br />

rrl<br />

154<br />

a<br />

J<br />

because you n'ili<br />

of r,6x1 resuits

Section II Part B Sample Examination <strong>Six</strong><br />

(b) F'ind the equation of the least squares regression line for predicting AP Exam<br />

grade based on annual grade. Interpret the slope estimate. Also find the value of<br />

the correlation coeffi cient.<br />

(c) Draw the residual plot. Does your plot indicate that this is a good linear fit?<br />

Explain.<br />

(D) Find the value of r' and explain its meaning in the context of these data.<br />

(E) Find the mean and the standard deviation of the annual grades and determine<br />

whether the data satisf, the Empirical Rule at one standard deviation. What do<br />

your findings imply? Are your findings supported by a graph of the data or by<br />

any characteristics of the data? Explain"<br />

155<br />

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