##### AP Statistics Final Exam

You record the age, marital status, and earned income of a sample of 1,463 women. The number and type of variables you have recorded is

A. 3 quantitative, 0 categorical

B. 4 quantitative, 0 categorical

C. 3 quantitative, 1 categorical

D. 2 quantitative, 1 categorical

D

Consumers Union measured the gas mileage in miles per gallon of 38 vehicles from the same model year on a special test track. The pie chart provides information about the country of manufacture of the model cars tested by Consumers Union. Based on the pie chart, we conclude

A. Japanese cars get significantly lower gas mileage than cars from other countries

B. U.S. cars get significantly higher gas mileage than cars from other countries

C. Mercedes, Audi, Porsche, and BMW represent approximately a quarter of the cars tested

D. more than half of the cars in the study were from the United States

D

Earthquake intensities are measured using a device called a seismograph, which is designed to be most sensitive to earthquakes with intensities between 4.0 and 9.0 on the Richter scale. Measurements of nine earthquakes gave the following readings.

L indicates that earthquake had an intensity below 4.0, and H indicates that the earthquake had an intensity above 9.0. The median earthquake intensity of the sample is

A. 5.75

B. 6.00

C. 6.47

D. 8.70

B

In a statistics class with 136 students, the professor records how much money (in dollars) each student has in his or her possession during the first class of the semester. This histogram shows the data that were collected.

The percentage of students with less than $10 in their possession is closest to

A. 30

B. 35

C. 50

D. 60

C

In a statistics class with 136 students, the professor records how much money (in dollars) each student has in his or her possession during the first class of the semester. This histogram shows the data that were collected.

Which of the following statements about this distribution is not correct?

A. the histogram is right-skewed

B. the median is less than $20

C. the IQR is $35

D. the histogram is unimodal

C

Forty students took a statistics examination having a maximum of 50 points. The score distribution is given in the following stem-and-leaf plot.

The third quartile of the score distribution is equal to

A. 45

B. 44

C. 43

D. 32

B

The mean salary of all female workers is $35,000. The mean salary of all male workers is $41,000. What must be true about the mean salary of all workers?

A. it must be $38,000

B. it must be larger than the median salary

C. it could be any number between $35,000 and $41,000

D. it must be larger than $38,000

C

A survey was designed to study how business operations vary according to their size. Companies were classified as small, medium, or large. Questionnaires were sent to 200 randomly selected businesses of each size. Since not all questionnaires in a survey of this type are returned, researched decided to investigate the relationship between the response rate and the size of the business.

What percent of all small companies receiving questionnaires responded?

A. 12.5%

B. 33.3%

C. 62.5%

D. 50.8%

C

A survey was designed to study how business operations vary according to their size. Companies were classified as small, medium, or large. Questionnaires were sent to 200 randomly selected businesses of each size. Since not all questionnaires in a survey of this type are returned, researched decided to investigate the relationship between the response rate and the size of the business.

Which of the following conclusions seems to be supported by the data?

A. there are more small companies than larger companies

B. small companies appear to have a higher response rate than medium or big companies

C. exactly the same number of companies responded as didn't respond

D. small companies dislike larger companies

B

A new experiment was conducted to investigate the effect of a new weed killer to prevent weed growth in onion crops. Two chemicals were used: the standard weed killer (C) and the new chemical (W). Both chemicals were tested at high and low concentration on a total of 50 test plots. The percent of weeds that grew in each plot was recorded. Here are some boxplots of the results.

Which of the following is *not *a correct statement about
the results of this experiment.

A. at both high and low concentrations, the new chemical (W) gives better weed control than the standard weed killer (C)

B. fewer weeds grew at higher concentrations of both chemicals

C. the results for the standard weed killer are less variable than those for the new chemical

D. high and low concentrations of either chemical have approximately the same effects on weed growth

D

Many professional schools require applicants to take a standardized test. Suppose that 1,000 students take such a test. Several weeks after the test, Pete receives his score report: he got a 63, which placed him at the 73rd percentile. This means that

A. Pete's score was below the median.

B. Pete did better than about 73% of the test takers.

C. Pete did worse than about 73% of the test takers.

D. Pete did better than about 63% of the test takers.

B

For the normal distribution show, the standard deviation is closest to

A. 0

B. 1

C. 2

D. 3

D

Rainwater was collected in water collectors at 30 different sites near an industrial complex, and the amount of acidity (pH level) was measured. The mean and standard deviation of the values are 4.60 and 1.10, respectively. When the pH meter was recalibrated back at the laboratory, it was found to be in error. The error can be corrected by adding 0.1 pH unites to all of the values and then multiplying the result by 1.2.

The mean and standard deviation of the corrected pH measurements are

A. 5.64, 1.44

B. 5.64, 1.32

C. 5.40, 1.44

D. 5.40, 1.32

B

The figure shows a cumulative relative frequency graph of the number of ounces of alcohol consumed per week in a sample of 150 adults. About what percent of these adults consume between 4 and 8 ounces per week?

A. 20%

B. 40%

C. 50%

D. 60%

B

The average yearly snowfall in Chillyvllle is normally distributed with a mean of 55 inches. If the snowfall in Chillyville exceeds 60 inches in 15% of the years, what is the standard deviation?

A. 4.83 inches

B. 5.18 inches

c. 6.04 inches

D. 8.93 inches

A

The figure show in a density curve of a distribution. Five of the
seven points marked on the density curve make up the five-number
summary for this distribution. Which two points are *not *part
of the five-number summary?

A. B and E

B. C and F

C. C and E

D. B and F

D

If the heights of American men follow a normal distribution, and 99.7% have heights between 5'0" and 7'0", what is your estimate of the standard deviation of the height of American men?

A. 1"

B. 3"

C. 4"

D. 6"

C

Which of the following is *not *correct about a standard
normal distribution?

A. the proportion of scores that satisfy 0 < z < 1.5 is 0.4332

B. the proportion of scores that satisfy z > 2.0 is 0.0228

C. the proportion of scores that satisfy z < 1.5 is 0.9332

D. the proportion of scores that satisfy z > -3.0 is 0.9938

D

Until the scale was changed in 1995, SAT scores were based on a scale set many years ago. For Math scores, the mean under the old scale in the 1990s was 470 and the standard deviation was 110. In 2009, the mean was 515 and the standard deviation was 116.

What is the standardized score (z-score) for a student who scored 500 on the old SAT scale?

A. -30

B. -0.13

C. 0.13

D. 0.27

D

Until the scale was changed in 1995, SAT scores were based on a scale set many years ago. For Math scores, the mean under the old scale in the 1990s was 470 and the standard deviation was 110. In 2009, the mean was 515 and the standard deviation was 116.

Jane took the SAT in 1994 and scored 500. Her sister Colleen took the SAT in 2009 and scored 530. Who did better on the exam, and how can you tell?

A. Colleen -- she scored 30 points higher than Jane

B. Colleen -- her standardized score is higher than Jane's

C. Jane -- her standardized score is higher than Colleen's

D. the two sisters did equally well -- their z-scores are the same

C

A school guidance counselor examines the number of extracurricular activities that students do and their grade point average. The guidance counselor says, "The evidence indicates that the correlation between the number of extracurricular activities a student participates in and his or her grade point average is close to zero." A correct interpretation of this statement would be that

A. active students tend to be students with poor grades, and vice versa

B. students with good grades tend to be students who are not involved in many extracurricular activities, and vice versa

C. students involved in many extracurricular activities are just as likely to get good grades as bad grades; the same is true for students involved in few extracurricular activities

D. there is no linear relationship between number of activities and grade point average for students at this school

D

The British government conducts regular surveys of household spending. The average weekly household spending (in pounds) on tobacco products and alcoholic beverages for each of 11 in Great Britain was recorded. A scatterplot of spending on alcohol versus spending on tobacco is show below. Which of the following statements is true?

A. there is clear evidence of a negative association between spending on alcohol and tobacco

B. the equation of the least-squares line for this plot would be approximately (y-hat) = 10-2x

C. the correlation for these date is r = 0.99

D. the observation in the lower-right corner of the plot is influential for the least-squares line

D

The fraction of variation in the values of y that is explained by the least-squares regression of y on x is

A. the correlation

B. the slope of the least-squares regression line

C. the square of the correlation coefficient

D. the residual

C

Which of the following statements is/are true?

I. If the student had used Calculator as the explanatory variable, the correlation would remain the same.

II. If the student had used Calculator as the explanatory variable, the slope of the least-squares line would remain the same.

III. The standard deviation of the number of correct answers on the paper-and-pencil quizzes was larger than the standard deviation on the calculator quizzes.

A. I only

B. II only

C. III only

D. I and III only

A

Scientists examined the activity level of fish at 7 different temperatures. Fish activity was rated on a scale of 0 (no activity) to 100 (maximal activity). The temperature was measured in degrees Celsius. A computer regression printout and a residual plot are given below. Notice that the horizontal axis on the residual plot is labeled "predicted (F/T)."

What was the activity level rating for fish at a temperature of 20.4C?

A. 86

B. 83

C. 80

D. 66

A

Scientists examined the activity level of fish at 7 different temperatures. Fish activity was rated on a scale of 0 (no activity) to 100 (maximal activity). The temperature was measured in degrees Celsius. A computer regression printout and a residual plot are given below. Notice that the horizontal axis on the residual plot is labeled "predicted (F/T)."

Which of the following gives a correct interpretation of *s
*in this setting?

A. for every 1C increase in temperature, fish activity is predicted to increase by 4.785 units

B. the average distance of the temperature readings from their mean is about 4.785C

C. the average distance of the activity level ratings from the least-squares line is about 4.785 units

D. the average distance of the activity level readings from their mean is about 4.785

C

Which of these is *not *true of the correlation r
between the lengths in inches and weights in pounds of a sample of
brook trout?

A. r must take a value between -1 and 1

B. r is measured in inches

C. if longer trout tend to also be heavier, the lengths of the trout in centimeters instead of inches

D. r would not change if we measured the lengths of the trout in centimeters instead of inches

B

When we standardize the values of variable, the distribution of standardized values has a mean 0 and standard deviation 1. Suppose we measure two variables X and Y on each of several subjects. We standardize both variables and then compute the least-squares regression line. Suppose the slope of the least-squares regression line is -0.44. We may conclude that

A. the correlation will be 1/-0.44

B. the intercept will be 1.0

C. the correlation will be 1.0

D. the correlation will also be -0.44

D

There is a linear relationship between the number of chirps made by the striped ground cricket and the air temperature. A least-squares fit of some data collected by a biologist gives the model (y-hat) = 25.2+3.3x, where is x is the number of chirps per minute and (y-hat) is the estimated temperature in degrees Fahrenheit. What is the predicted increase in temperature for an increase of 5 chirps per minute?

A. 3.3F

B. 16.5F

C. 25.2F

D. 28.5F

B

A data set included the number of people per television set and the number of people per physician for 40 countries. The Fathom screen shot below displays a scatterplot of the data with the least-squares regression line added. In Ethiopia, there were 503 people per TV and 36,660 people per doctor. What effect would removing this point have on the regression line?

A. slope would increase; y intercept would increase

B. slope would increase; y intercept would decrease

C. slope would decrease; y intercept would increase

D. slope and y intercept would stay the same

C

When we take a census, we attempt to collect data from

A. a stratified random sample

B. every individual chosen in a simple random sample

C. every individual in the population

D. a voluntary response sample

C

You want to take a simple random sample (SRS) of 50 of the 816 students who live in a dormitory on campus. You label the students 001 to 816 in alphabetical order. In the table of random digits, you read the entries

95592 94007 69769 33547 72450 16632

The first three students in your sample have labels

A. 955, 929, 400

B. 400, 769, 769

C. 929, 400, 769

D. 400, 769, 335

D

A study of treatments for angina (pain due to low blood supply to the heart) compared bypass surgery, angioplasty, and use of drugs. The study looked at the medical records of thousands of angina patients whose doctors had chosen one of these treatments. It found that the average survival time of patients given drugs was the highest. What do you conclude?

A. this study proves that drugs prolong life and should be the treatment of choice

B. we can conclude that drugs prolong life because the study was a comparative experiment

C. we can't conclude that drugs prolong life because no placebo was used

D. we can't conclude that drugs prolong life because this was an observational study

D

A simple random sample (SRS) is

A. any sample selected by using chance

B. any sample that gives every individual the same chance to be selected

C. a sample that gives every possible sample of the same size the same chance to be selected

D. a sample that doesn't involve strata or clusters

C

Consider an experiment to investigate the effectiveness of different insecticides in controlling pests and their impact on the productivity of tomato plants. What is the best reason for randomly assigning treatment levels (spraying or not spraying) to the experimental units (farms)?

A. random assignment makes the experiment easier to conduct since we can apply the insecticide in any pattern rather than in a systematic fashion

B. random assignment will tend to average out all other uncontrolled factors such as soil fertility so that they are not confounded with the treatment effects

C. random assignment makes the analysis easier since the data can be collected and entered into the computer in any order

D. random assignment is required by statistical consultants before they will help you analyze the experiment

B

The most important advantage of experiments over observational studies is that

A. experiments are usually easier to carry out

B. experiments can give better evidence of causation

C. confounding cannot happen in experiments

D. an observational study cannot have a response variable

B

A TV station wishes to obtain information on the TV viewing habits in its market area. The market area contains one city of population 170,000, another city of 70,000, and four towns of about 5,000 inhabitants each. The station suspects that the viewing habits may be different in larger and smaller cities and in the rural areas. Which of the following sampling designs would give the type of information that the station requires?

A. a cluster sample using the cities and towns as clusters

B. a convenience sample from the market area

C. a simple random sample from the whole market area

D. a stratified sample from the cities and towns in the market area

D

*Bias* in a sampling method is

A. any error in the sample result, that is, any deviation of the sample result from the truth about the population

B. the random error due to using chance to select a sample

C. racism or sexism on the part of those who take the sample

D. any systematic error that tends to occur in the same direction whenever you use this sampling method

D

You wonder if TV ads are more effective when they are longer or repeated more often or both. So you design an experiment. You prepare 30-second and 60-second ads for a camera. Your subjects watch the same TV programs, but you assign them at random to four groups. One group sees the 30-second ad once during the program; another sees it three times' the third group sees the 60-second ad once; and the last group sees the 60-second ad three times. You ask all subjects how likely they are to buy the camera.

A. this is a randomized block design, but not a matched pairs design

B. this is a matched pairs design

C. this is a completely randomized design with one explanatory variable (factor)

D. this is a completely randomized design with two explanatory variables (factors).

D

A researcher wishes to compare the effects of 2 fertilizers on the yield of soybeans. She has 20 plots of land available for the experiment and she decides to use a matched pairs design with 10 pairs of plots. To carry out the random assignment for this design, the researcher should

A. use a table of random numbers to divide the 20 plots into 10 pairs and then, for each pair, flip a coin to assign the fertilizers to the 2 plots

B. subjectively divide the 20 plots into 10 pairs (making the plots within a pair as similar as possible), and then, for each pair, flip a coin to assign the fertilizers to the 2 plots

C. use a table of random numbers to divide the 20 plots into 10 pairs and then use the table of random numbers a second time to decide upon the fertilizer to be applied to each member of the pair

D. flip a coin to divide the 20 plots into 10 pairs and then, for each pair, use a table of random numbers to assign the fertilizers to the 2 plots

B

You want to know the opinions of American high school teachers on the issue of establishing a national proficiency test as a prerequisite for graduation from high school. You obtain a list of all high school teachers belonging to the National Education Association (the country's largest teachers' union) and mail a survey to a random sample of 2,500 teachers. In all, 1,347 of the teachers return the survey. Of those who responded, 32% say that they favor some kind of national proficiency test. Which of the following statements about this situation is true?

A. since random sampling was used, we can feel confident that the percent of all American high school teachers who would say they favor a national proficiency test is close to 32%

B. we cannot trust these results, because the survey was mailed. Only survey results from face-to-face interviews are considered valid

C. the results of this survey may be affected by a nonresponse bias

D. the results of this survey cannot be trusted due to voluntary response bias

C

Dr. Stats plans to toss a fair coin 10,000 times in the hope that it will lead him to a deeper understanding of the laws of probability. Which of the following statements is true?

A. it is unlikely that Dr. Stats will get more than 5,000 heads

B. whenever Dr. Stats gets a string of 15 tails in a row, it becomes more likely that the next toss will be a head

C. the fraction of tosses resulting in heads should be closed to 1/2

D. the chance that the 100th toss will be a head depends somewhat on the results of the first 99 tosses

C

China has 1.2 billion people. Marketers want to know which international brands they have heard of. A large study showed that 62% of all Chinese adults have heard of Coca-Cola. You want to simulate choosing a Chinese at random and asking if he or she has heard of Coca-Cola. One correct way to assign random digits to simulate the answer is

A. one digit simulates one person's answer; odd means "yes" and even means "no"

B. one digit simulates a person's answer; 0 to 6 mean "yes" and 7 to 9 mean "no"

C. one digit simulates the result; 0 to 9 tells how many in the sample said "yes"

D. two digits simulate one person's answer; 00 to 62 mean "yes" and 63 to 99 mean "no"

D

Choose an American household at random and record the number of vehicles they own. Here is the probability model if we ignore the few households that own more than 5 cars. A housing company builds houses with two-car garages. What percent of households have more cars than the garage can hold?

A. 7%

B. 13%

C. 20%

D. 45%

C

Computer voice recognition software is getting better. Some companies claim that their software correctly recognizes 98% of all words spoken by a trained user. To simulate recognizing a single word when the probability of being correct is 0.98, let two digits simulate one word; 00 to 97 mean "correct." The program recognizes words (or not) independently. To simulate the programs performance on 10 words, use these random digits:

60970 70024 17868 29843 61790 90656 87964 18883

The number of words recognized correctly out of the 10 is

A. 10

B. 9

C. 8

D. 7

B

One thousand students at a city high school were classified according to both GPA and whether or not they consistently skipped classes. The two-way table below summarizes the data.

What is the probability a student has a GPA under 2.0?

A. 0.277

B. 0.255

C. 0.450

D. 0.475

B

One thousand students at a city high school were classified according to both GPA and whether or not they consistently skipped classes. The two-way table below summarizes the data.

What is the probability that a student has a GPA under 2.0 or has skipped many classes?

A. 0.08

B. 0.281

C. 0.285

D. 0.365

C

One thousand students at a city high school were classified according to both GPA and whether or not they consistently skipped classes. The two-way table below summarizes the data.

What is the probability that a student has a GPA under 2.0 given that he or she has skipped many classes?

A. 0.080

B. 0.285

C. 0.314

D. 0.727

D

For events A and B related to the same chance process, which of the following statements is true?

A. if A and B are mutually exclusive, then they must be independent

B. if A and B are independent, then they must be mutually exclusive

C. if A and B are independent, then they cannot be mutually exclusive

D. if A and B are not independent, then they must be mutually exclusive

C

Choose an American adult at random. The probability that you choose a woman is 0.52. The probability that the person you choose has never been married is 0.25. The probability that you chose a woman who has never been married is 0.11. The probability that the person you choose is either a woman or has never been married (or both) is therefore about

A. 0.77

B. 0.66

C. 0.44

D. 0.38

A

A deck of playing cards has 52 cards, of which 12 are face cards. If you shuffle the deck well and turn over the top 3 cards, one after the other, what's the probability that all 3 cards are face cards?

A. 0.001

B. 0.05

C. 0.010

D. 0.012

C