AP STATS Exam

2. Which of the following is a true statement? a. All symmetric histograms have single peaks. b. All symmetric bell-shaped curves are normal. c. All normal curves are bell-shaped and symmetric. d. The smaller the value of df, the close a t-distribution is to being normal. e. None of the above are true statements.

c. All normal curves are bell-shaped and symmetric.

6) Given these parallel boxplots, which of the following is incorrect? a. The ranges are the same b. The interquartile ranges are the same c. Both sets are skewed to both lower and higher values d. Set A may not be symmetric e. Set A may have 100 times as many values as set B

c. Both sets are skewed to both lower and higher values

) The amount of Omega 3 fish oil in capsules labeled 1,000 mg is measured for four manufacturers' products yielding for the following: Which of the manufacturers' samples has the smallest range? a. A b. B c. C d. D e. There is insufficient information to answer

c. C

7) Which of the following is a true statement? a. Stemplots are useful both for quantitative and categorical data sets b. Stemplots are equally useful for small and very large data sets c. Stemplots can show symmetry, gaps, clusters, and outliers d. Stems should be skipped only if there is no data value for particular stem e. Whether or not to provide a key depends upon the relative importance of the data being displayed

c. Stemplots can show symmetry, gaps, clusters, and outliers

2) Suppose a manufacturer knows that 20 percent of the circuit boards coming off the assembly line have a minor defect. If an inspector keeps inspecting boards until he comes upon one with the defect, what is the probability he will have to inspect at most three boards? a) .128 b) .384 c) .488 d) .512 e) .896

c) .488

5. Three fair coins are tossed. If all land "heads," the player wins $10, and if exactly two land heads, the player wins $5. If it costs $4 to play, what is the player's expected outcome after four games? a) Loss of $0.875 b) Loss of $1.00 c) Loss of $3.50 d) Win of $2.25 e) Wing of $9.00

c) Loss of $3.50

3. Which of the following distributions has a mean of 60 and a standard deviation of 4?

(A)

3. Suppose you wish to compare the average height of math/science teachers to the average height of English/social studies teachers in your high school. Which is the most appropriate technique for gathering the needed data? (A) Census (B) Sample survey (C) Experiment (D) Observational study (E) None of these methods is appropriate

(A) Census

1. An advantage to using surveys as opposed to experiments is that (A) Surveys are generally cheaper to conduct (B) Its generally easier to conclude cause and effect from surveys (C) Surveys are generally not subject to bias (D) Surveys involve use of randomization (E) Surveys can make use of stratifications

(A) Surveys are generally cheaper to conduct

The company has 55 employees.... involves dot plots

Answer is A

1. The table below shows the number of students referred for disciplinary reasons to the principal's office, broken down by the day of the week. A counselor would like to know if such referrals are related to the day of the week. What is the value of chi-square for the appropriate test? Monday Tuesday Wednesday Thursday Friday 12 5 9 4 15

Answer: B

4) In which of the following histograms is the mean less than the median?

Answer: C

8) To which of the boxplots can the above histogram correspond?

Answer: D

9. Two confidence interval estimates from the same sample are (72.2, 77.8) and (71.3, 78.7). One estimate is at the 95 percent level, and the other is at the 99 percent level. Which is which? A. (72.2, 77.8) is the 95 percent level B. (72.2, 77.8) is the 99 percent level C. This question cannot be answered without knowing the sample size D. This question cannot be answered without knowing the sample standard deviation E. This question cannot be answered without knowing both the sample size and standard deviation

A. (72.2, 77.8) is the 95 percent level

2) A mortgage company advertises that 85 percent of applications are approved. In a random sample of 30 applications, what is the expected number that will be turned down? A) 30(.85) B) 30(.15) C) 30(.85)(.15) D) √30(.85)(.15) E) √(.85)(.15)/30

B) 30(.15)

8) Suppose the average outstanding loan for college graduates is $23,500 with a standard deviation of $7,200. In an SRS of 50 graduating college students, what is the probability that their mean outstanding loan is under $21,000? A. .0000 B. .0070 C. .0141 D. .03637 E. .9930

B. .0070

2. A national parent organization is concerned that middle school student are spending too much time (more than 8 hours per week) with home video game consoles like the Xbox 360, Wii, and Play Station 3. A study is conducted sampling 150 students, and the resulting sample mean is 7.95 hours. What is the appropriate alternative hypothesis for this study? A.) Ha: µ < 8 B.) Ha: µ > 8 C.) Ha: µ < 7.95 D.) Ha: µ > 7.95 E.) Ha: µ≠ 7.95

B.) Ha: µ > 8

4. A weight loss program had the participants eat different types of fiber (bran, gum, or a control cracker) before each meal. All participants experienced either high, medium, or low weight loss. The resulting contingency table is given below. Low Medium High Bran 23 15 12 Gum 14 18 18 Control 27 14 9 With a chi-square value of 7.49 is there statistical evidence of a relationship between type of bran and amount of weight loss? A.)No, because the P-value is greater than .10. B.) Yes, .05<P<.10, indicating some evidence of a relationship. C.) Yes, .01<P<.05, indicating evidence of a relationship. D.) Yes, .001<P<.01, indicating strong evidence of a relationship. E.) Yes, P<.001 indicating very strong evidence of a relationship.

B.) Yes, .05<P<.10, indicating some evidence of a relationship.

6. A company bids on three independent contracts with probabilities of winning the contracts .1, .25, and .3, respectively. What is the probability of winning at least one contract? A) .35 B) .4725 C) .5275 D) .65 E) .9925

C) .5275

8. Car insurance policies for teenagers have higher premiums than for adult drivers because teenagers are considered to be a high-risk population. Suppose the average yearly cost of teenage (ages 16-19) insurance is $3,025 with a standard deviation of $430. Is there sufficient information to answer either or both of the questions: I. What is the probability that a randomly chosen teenage driver pays over $3,000 a year for auto insurance? II. What is the probability that the average amount paid in an SRS of 50 teenage drivers is more than $3,000 a year? A) Insufficient information to answer either question. B) Sufficient information to answer question I, but not question II. C) Sufficient information to answer question II, but not question I. D) Sufficient information to answer both questions. E) With a sample size of 50, the sampling distribution is approximately normal with mean $3,025 and standard deviation $430/√50.

C) Sufficient information to answer question II, but not question I.

3. A confidence interval estimate is determined from the summer earnings of an SRS of n students. All other things being equal, which of the following will result in a smaller margin of error? A. A greater confidence level B. A larger sample standard deviation C. A larger sample size D. Accepting less precision E. Introducing bias into sampling

C. A larger sample size

8. Suppose (48, 65) is a 95 percent confidence interval estimate for a population mean µ. Which of the following is a true statement? A. There is a .95 probability that µ is between 48 and 65. B. If 100 random samples of the given size are picked and a 95 percent confidence interval estimate is calculated from each, then µ will be in 95 of the resulting intervals C. If 95 percent confidence intervals are calculated from all possible samples of the given size, µ will be in 95 percent of these intervals D. The probability that µ is in any particular confidence interval can be any value between 0 and 1 E. Confidence level cannot be interrupted until after data is obtained

C. If 95 percent confidence intervals are calculated from all possible samples of the given size, µ will be in 95 percent of these intervals

10) The average noise level in a bar is 36 decibels with a standard deviation of 5 decibels. Assuming a normal distribution, what is the probability the noise level is between 30 and 40 decibels? A. .327 B. .337 C. .381 D. .673 E. .683

D. .673

10. A congressional representative serving on the Joint Committee on Taxation states that the average yearly charitable contributions for taxpayers is $1,250. A lobbyist for a national church organization who believes that the real figure is lower samples 12 families and comes up with a mean of $1,092 and a standard deviation of $308. Where is the P-value? A. Below .01 B. Between .01 and .025 C. Between .025 and .05 D. Between .05 and .10 E. Over .10

D. Between .05 and .10

7) Which of the following are true statements? I. The area under a normal curve is always equal to 1, no matter what the mean and standard deviation are. II. The smaller the standard deviation of a normal curve, the higher and narrower the graph III. Normal curves with different means are centered around different numbers A. I and II B. I and III C. II and III D. I, II, and III E. None of the above gives the complete set of true responses

D. I, II, and III

5) An inspection procedure at a manufacturing plant involves picking three items at random and then accepting the whole lot if at least two of the three items are in perfect condition. If in reality 84 percent of the whole lot are perfect, what is the probability that the lot will be accepted? A) .560 B) .593 C) .667 D) .706 E) .931

E) .931

1) Population P1 and P2 are normally distributed and have identical means. However, the standard deviation of P1 is twice the standard deviation of P2. What can be said about the percentage of observations falling within two standard deviations of the mean for each population? A) The percentage for P1 is twice the percentage for P2 B) The percentage for P1 is greater, but not twice as great, as the percentage for P2 C) The percentage for P2 is twice the percentage for P1 D) The percentage for P2 is greater, but not twice as great, as the percentage for P1 E) The percentage are identical

E) The percentage are identical

7. In 1798 Henry Cavendish used a torsion balance to estimate the density of the Earth as 5.42 times the density of water. A modern day geologist runs a hypothesis test with Ha: m ≠ 5.42 and obtained a P-value of .08. If the geologist had run a one-sided test with the same data, what is true about the possible resulting P-value(s)? A) The only possible P-value is 0.4. B) The only P-value is .08. C) The only possible P-value is .16. D) The possible P-values are .04 and .92. E) The possible P-values are .04 and .96.

E) The possible P-values are .04 and .96.

9. The 40 yard dash is an important diagnostic evaluation tool for all positions in both collegiate an professional football recruiting. Which of the following is the best interpretation of a 95 percent confidence interval of (4.67, 4.87) seconds for the mean 40 yard dash time? A) Ninety-five percent of all players run the 40 yard dash in between 4.67 and 4.87 seconds. B) Ninety-five percent of all players have a mean 40 yard dash time between 4.67 and 4.87 seconds. C) Players run the 40 yard dash in between 4.67 and 4.87 seconds 95 percent of the time. D) We are 95 percent confident that for any given player his 40 yard dash time is between 4.67 and 4.87 seconds. E) We are 95 percent confident that the mean 40 yard dash time is between 4.67 and 4.87 seconds.

E) We are 95 percent confident that the mean 40 yard dash time is between 4.67 and 4.87 seconds.

7. Under what conditions would it be meaningful to construct a confidence interval estimate when the data consist of the entire population. A. If the population size is small (n<30) B. If the population size is large (n≥30) C. If a higher level of confidence is desired D. If the population is truly random E. Never

E. Never

9) The are five outcomes to an experiment and a student calculates the respective probabilities of the outcomes to be .34, .50, .42, 0, and -.26. The proper conclusion is that A. The sum of the individual probabilities is 1 B. One of the outcomes will never occur C. One of the outcomes will occur 50 percent of the time D. All of the above are true E. The student made an error

E. The student made an error

3. During one of the recent fiscal controversies, only 18 percent of Americans approved of the job Congress was doing. A national polling organization wants to construct a 99 percent confidence interval of the current percent with a margin of error of ±2 percent. Assuming that the current percent is roughly what it was before, which of the following will lead to a correct calculation of sample size n? A.) (2.326)√(0.5)(0.5)/n ≤ .02 B.) (2.576)√(0.5)(0.5)/n ≤ .01 C.) (2.326)√(0.18)(0.82)/n ≤ .01 D.) (2.576)√(0.18)(0.82)/n ≤ .01 E.) (2.576 )√(0.18)(0.82)/n ≤ .02

E.) (2.576 )√(0.18)(0.82)/n ≤ .02

7) Apples growing in a certain orchard have weights that are normally distributed with a standard deviation of 2.2 ounces. What is the mean weight if 80 percent of he apples weigh less than 9.1 ounces? a) 7.25 ounces b) 7.45 ounces c) 7.72 ounces d) 10.95 ounces e) The mean cannot be computed from the information given.

a) 7.25 ounces

6) Which of the histograms represents the sampling distribution of for p = .7 and n = 84? a) this one b) c) d) e)

a) this one

4. Given these parallel boxplots, which of the following is true? a. All three distributions have the same range. b. All three distributions have the same interquartile range. c. All three medians are between 9 and 13. d. All three distributions appear to be skewed right. e. All three distributions can reasonably be assumed to be of sample from normally

a. All three distributions have the same range.

2. A histogram of the educational level (in number of years of schooling) of the adult population of the United States would probably have which of the following characteristics? a. Symmetry b. Clusters around 8, 12, and 16 years c. A gap around 12 years d. Skewness to the right e. A normal distribution

b. Clusters around 8, 12, and 16 years

9) Among the 125 teachers at a small college, 75 are registered Democrats, 35 are registered Republicans, and the rest are independents. If a 10-person committee is randomly picked, what is the probability that at least two independents are chosen. a) 2 8 b) c) d) e) None of these are correct

c)

4) The mean income per household in a certain state is $28,000 with a standard deviation of $8,500. Assuming a normal distribution, 95 percent of all households have an income over what amount? a) $11,000 b) $11,300 c) $14,000 d) $19,500 e) $42,000

c) $14,000

8) The number of hybrid cars a dealer sells has the following probability distribution: Number of hybrids 0 1 2 3 4 5 Probability .32 .28 .15 .11 .08 .06 The dealer purchases the cars for $21,000 and sells them for $24,500. What is the expected weekly profit from selling hybrid cars? a) $2,380 b) $3,500 c) $5,355 d) $8,109 e) $37,485

c) $5,355

3) A teacher is teaching two AP Statistics classes. On the final exam, the 25 students in the first class averaged 87, while the 30 students in the second class averaged 98. If the teacher combines the classes, what will the average final exam score be? a. 92 b. 92.5 c. 93 d. 94.5 e. 95

c. 93

10) There are 8,253 men and 10,327 women at a state university. If 43 percent of the men and 27 percent of the women are business majors, what is the expected number of business majors in a random sample of 200 students? a) 31.7 b) 34.1 c) 63.4 d) 68.2 e) 70.0

d) 68.2

3) A new soft drink product has an average number of 77 calories per bottle with a standard deviation of 4.5 calories. In a random sample of 40 bottles, what is the probability that the mean number of calories is between 75 and 80? a) .4191 b) .4975 c) .5000 d) .8383 e) .9975

e) .9975

7. A newspaper advice columnist asks her readers if they would have married their current spouse if they had it to do over again. Of the 25,000 or so responses, 80 percent said no. What does this show? (A) The survey is meaningless because of voluntary response bias (B) No meaningful conclusion is possible without knowing something more about the characteristics of her readers (C) The survey would have been more meaningful if she had picked a random sample of the 25,000 readers who responded (D) The survey would have been more meaningful if she had used a control group (E) This was a legitimate sample, randomly drawn from her readers, and of sufficient size to allow the conclusion that most of her readers who are married would have second thoughts about marrying their current spouse

(A) The survey is meaningless because of voluntary response bias

10. In general, for a survey to yield usable results: (A) A sample size of n=30 is usually sufficient (B) Researchers must be careful in the way questions are worded (C) Researchers must carefully choose people who they think are representative of the population (D) A census is the only truly accurate methodology (E) Sampling error must be avoided

(B) Researchers must be careful in the way questions are worded

2. In a study of Parkinson's disease, 100 volunteers had incinsions made through their skulls. The patients were randomly sorted into two groups, one of which had a new drug inserted into the brain. In the other group, skulls were closed with no treatment given. The patients did not know who received the drug. In the weeks to follow all 100 volunteers showed similar improvement in physical condition. What is this an example of? (A) The effect of a treatment unit (B) The placebo effect (C) The control group effect (D) Sampling error (E) Voluntary response bias

(B) The placebo effect

9. What is bias in conducting surveys? (A) An example of sampling error (B) Lack of a control group (C) Confounding variables (D) Difficulty in concluding cause and effect (E) A tendency to favor the selection of certain members of a population

(E) A tendency to favor the selection of certain members of a population

6. Which of the following is a true state about blocking? (A) Blocking is to experiment design as stratification is to sampling design. (B) Be controlling certain variables, blocking can make conclusions more specific. (C) The paired (matched pairs) comparison design is a special case of blocking. (D) Blocking is a useful procedure when there are certain attributes, not under study, which may affect the outcomes. (E) All of the above are true statements about blocking.

(E) All of the above are true statements about blocking. (E) All of the above are true statements about blocking.

8. Which of the following is most important in minimizing the placebo effect? (A) Replication and randomization (B) Replication and blinding (C) Randomization and blinding (D) Randomization and a control (E) Blinding and a control

(E) Blinding and a control

5. A human resources department plans to survey 100 of the 3,000 employees in the firm. An alphabetical list of the employees is available, a random number between 1 and 30 is picked, and the sample consists of the person that far down the list together with every 30th person after that. This procedure is an example of which type of sampling? (A) Cluster (B) Convenience (C) Simple random (D) Stratified (E) Systematic

(E) Systematic

4. Sampling error is (A) The mean of a sample statistic (B) The standard deviation of a sample statistic (C) The standard error of a sample statistic (D) The result of bias (E) The difference between a population parameter and an estimate of that parameter

(E) The difference between a population parameter and an estimate of that parameter

6) A piece of clothing takes an average of 38 minutes to move through an assembly line. If the standard deviation is 4 minutes, and the distribution is normal. What is the probability that a piece of clothing will take over 45 minutes? A) .040 B) .080 C) .175 D) .227 E) .460

A) .040

2. Which of the following is a true statement? A. Tests of significance (hypothesis tests) are designed to measure the strength of evidence against the null hypothesis. B. A well-planned test of significance should result in a statement either that the null hypothesis is true or that it is false. C. The null hypothesis is one-sided and expressed using either < or > if there is interest in deviations in only one direction. D. When a true parameter value is farther from the hypothesized value, it becomes easier to reject the alternative hypothesis E. Increasing the sample size makes it more difficult to conclude that an observed difference between observed and hypothesized values is significant.

A. Tests of significance (hypothesis tests) are designed to measure the strength of evidence against the null hypothesis.

1. Is there a home field advantage in professional baseball games? Emotional support from the fans and familiarity with the field seem to make a difference as the home team has won in approximately 5/9 of World Series games. Assuming this probability is constant and games are independent, if the home team wins the first game, what is the probability that the home team also wins the next two games? A.) (5/9)^2 B.) (5/9)^3s C.) 3(5/9)^2(4/9) D.) 1-(5/9)^3 E.) 1-(4/9)^2

A.) (5/9)^2

6. City planners are trying to decide among various parking plan options ranging from more on-street spaces to multilevel parking garages. Before they make a decision, they wish to test the downtown merchants' claim that shoppers park for an average of only 38 minutes. The planners have decided to tabulate parking durations for an SRS of 100 shoppers and reject the merchants' claim if the sample mean exceeds 40 minutes. If the merchants' claim is wrong, and the true mean is 43 minutes, what is the probability that the random sample will lead to a mistaken failure to reject the merchants' claim? Assume that the standard deviation in parking durations is 12 minutes.

Answer: C

4. In a random sample of 1,250 adult drivers, 450 said that they would cut their driving by 10 percent if this significantly helped the environment. Find a 95 percent confidence interval estimate of the proportion of adult drivers who are willing to cut their driving by 10 percent to help the environment.

Answer: D

5. Four math majors received the following salary offers upon graduation: $48,000, $55,000, $42,000, and $51,000. Assuming all assumptions are met, establish a 95 percent confidence interval for the population mean.

Answer: E

0. Babe Ruth had a career batting average of p= .342, pretty amazing for a player known for his homeruns! Consider two random samples, one of 30 at bats and one of 60 at-bats. Which of the following is an incorrect statement about the sampling distribution for p with n=30 and 60? A) The shape of the sampling distribution for n=60 is closer to a normal distribution than that for n=30. B) The mean of the sampling distribution for n=60is larger than that for n=30. C) The standard deviation of the sampling distribution for n=60 is less than that for n=30. D) The mean of the sampling distribution for p is equal to the expected number of hits divided by the sample size. E) The standard deviation of the sampling distribution for p is equal to the standard deviation for the expected number of hits divided by the sample size.

B) The mean of the sampling distribution for n=60is larger than that for n=30.

4) A person has a 10 percent chance of wining the daily office lottery. What is the probability she wins on the fourth day? A) (4 1) (.10)3(.90) B) (4 3) (.10)(.90)3 C) (.10)3(.90) D) (.10)(.90)3 E) None of the above give the correct probability

D) (.10)(.90)3

3) The following is from a particular region's mortality table. Age 0 20 40 60 80 Number Surviving 10,000 9,700 9,240 7,800 4,300 What is the probability that a 20-year-old will survive to be 60? A) .1959 B) .4419 C) .7800 D) .8041 E) .9700

D) .8041

1) Given this cumulative plot, and using the most commonly accepted definition of outliers, what ages would be considered outliers? a. Between 20 and 25 b. Between 20 and 30 c. Between 20 and 40 d. Between 20 and 25, or between 55 and 60 e. Between 20 and 30, or between 50 and 60

a. Between 20 and 25

10) Given this back-to-back stemplot, which of the following is incorrect? a. The distributions have the same mean b. The distribution have the same range c. The distributions have the same interquartile range d. The distributions have the same standard deviation e. The distributions have the same variance

a. The distributions have the same mean

4. A data set includes two outliers, one at each end. If both these outliers are removed, which of the following is a possible result? a. Both the mean and standard deviation remain unchanged. b. Both the median and standard deviation remain unchanged. c. Both the standard deviation and variance remain unchanged. d. Both the mean and median remain unchanged. e. Both the mean and standard deviation increase.

d. Both the mean and median remain unchanged.

3. A doctor wishes to compare the resting heart rates of his younger patients (younger than 30 years old) versus his older patients (older than 30 years old). Which of the following graphical displays is inappropriate? a. Back-to-back stemplot b. Parallel boxplots c. Side-by-side histograms d. Scatterplot e. All the above displays are appropriate

d. Scatterplot

1. When there are multiple gaps and clusters, which of the following is the best choice to give an overall picture of a distribution? a. Mean and standard deviation b. Median and interquartile range c. Boxplot with its five-number summary d. Stemplot or histogram e. None of the above are really helpful in showing gaps and clusters

d. Stemplot or histogram

1) Suppose we have a binomial random variable where the probability of exactly four successes is () p4 (.37)7. What is the mean of the distribution? a) 2.52 b) 2.59 c) 4.07 d) 4.41 e) 6.93

e) 6.93

5) If every man married a woman who was exactly 3 years younger than he, what would be the correlation between the ages of married men and women? a. Somewhat negative b. 0 c. Somewhat positive d. Nearly 1 e. 1

e. 1

2) Given the above two histograms, which of the following statements is incorrect? a. Both sets have the same mean b. Both sets have the same median c. Both sets have the same range d. Set A has a greater variance than does set B e. Each set has approximately 12 elements (6 under and 6 over the median)

e. Each set has approximately 12 elements (6 under and 6 over the median)

1. When a set of data has suspect outliers, which of the following are preferred measures of central tendency and of variability? a. Mean and standard deviation b. Mean and variance c. Mean and range d. Median and range e. Median and interquartile range

e. Median and interquartile range

5. Given this histogram, and using the most commonly accepted definition of outliers, what values would be considered outliers? a. Between 115 and 120 b. Between 110 and 120 c. Between 50 and 55, or between 115 and 120 d. Between 50 and 55, or between 110 and 120 e. There are no outliers

e. There are no outliers