AP Stats Multiple Choice

A company sponsoring a new Internet search engine wants to collect date on the ease of using it. Which is the best way to collect data?

a. census
b. sample survey
c. observational study
d. experiment
e simulation

b. sample survey
The January 2005 Gallup Youth Survey telephone a random sample of 1,028 U.S. teens and asked these teens to name their favorite movie from 2004. NAPOLEON DYNAMITE had the highest percentage with 8% of teens ranking it as their favorite movie. Which is true?
I. The population of interest is all U.S. teens
II. 8% is a statistic and not the actual percentage of all U.S. teens who would rank this movie as their favorite.
III. This sampling design should provide a reasonably accurate estimate of the actual percentage of all U.S. teens who would rank this movie as their favorite.

a. I only
b. II only
c. III only
d. I and II
e. I, II, and III

e. I, II, and III
Suppose your local school district decides to randomly test high school students for attention deficit disorder (ADD). There are there high schools in the district, each with grades 9-12. The school board pools all of the students together and randomly samples 250 students. Is this a simple random sample?

a. Yes, because the students were chosen at random
b. Yes, because each student is equally likely to be chosen
c. Yes, because they could have chosen any 250 students from throughout the district
d. No, because we can’t guarantee that there are students from each school in the sample
e. No, because we can’t guarantee that there are students from each grade in the sample

c. Yes, because they could have chosen any 250 students from throughout the district
A basketball player has a 70% free throw percentage. Which plan could be used to simulate the number of free throws she will make in her next five free throw attempts?

I. Let 0,1 represent making the first shot and 2,3 represent making the second shot…..8,9 represent making the fifth shot. Generate five random numbers 0-9 ignoring repeats
II. Let 0,1,2 represent missing a shot and 3,4….,9 represent making a shot. Generate five random numbers 0-9 and count how many numbers are in 3-9
III. Let 0,1,2 represent missing a shot and 3,4….,9 represent making a shot. Generate five random numbers 0-9 and count how many numbers are in 3-9, ignoring repeats

a. I only
b. II only
c. III only
d. II and III
e I, II, and III

b. II only
More dogs are being diagnosed with thyroid problems than have been diagnosed in the past. A researcher identified 50 puppies without thyroid problems and kept records of their diet for several years to see if any developed thyroid problems. This is a(n)

a. randomized experiment
b. survey
c. prospective study
d. retrospective study
e. blocked experiment

c. prospective study
A chemistry professor who teaches a large lecture class surveys his students who attend his class about how he can make the class more interesting, hoping he can get more students to attend. This survey method suffers from

a. voluntary response bias
b. nonresponse bias
c. response bias
d. undercoverage
e. none of the above

d. undercoverage
Placebos are a tool for

a. sampling
b. blocking
c. blinding
d. control
e. randomization

c. blinding
Double-blinding in experiments is important so that

I. The evaluators do not know which treatment group the participants are in
II. The participants do not know which treatment group they are in
III. No one knows which treatment any of the participants are getting

a. I only
b. II only
c. III only
d. I and II
e. I, II, and III

d. I and II
Which of the following is NOT required in an experimental design?

a. blocking
b. control
c. randomization
d. replication
e. all are required in an experimental design

a. blocking
A researcher wants to compare the effect of a new type of shampoo on hair condition. The researcher believes that men and women may react differently to the shampoo. Additionally, the researcher believes that the shampoo will react differently on hair that is dyed. The subjects are split into four groups: men who dye their hair; men who do not dye their hair; women who dye their hair; women who do not dye their hair. Subjects in each group are randomly assigned to the new shampoo and the old shampoo. This experiment

a. is completely randomized
b. has three factors (shampoo type, gender, whether hair is dyed)
c. has two factors (shampoo type and whether hair is dyed) blocked by gender
d. has two factors (gender and whether hair is dyed) blocked by shampoo type
e. has one factor (shampoo type), blocked by gender and whether hair is dyed

b. has three factors (shampoo type, gender, whether hair is dyed)
Researchers studying growth patterns of children collect data on the heights of fathers and sons. The correlation between the fathers’ heights and the heights of the 16 year-old sons is most likely to be

a. near -1.0
b. near 0
c. near +0.7
d. exactly +1.0
e. somewhat greater than 1.0

c. near +0.7
The auto insurance industry crashed some test vehicles into a cement barrier at speeds of 5 to 25 mph to investigate the amount of damage to the cars. They found a correlation of r=0.60 between speed (MPH) and damage ($). If the speed at which the car hit the barrier is 1.5 standard deviations above the mean speed, we expect the damage to be ______ the mean damage.

a. equal to
b. 0.36 SD above
c. 0.60 SD above
d. 0.90 SD above
e. 1.5 SD above

d. 0.90 SD above (SDxr=A)
The correlation between X and Y is r=0.35. If we double each X value, decrease each Y by 0.20, and interchange the variables (put X on the Y-axis and vice versa) the new correlation

a. is 0.35
b. is 0.50
c. is 0.70
d. is 0.90
e. cannot be determined

a. is 0.35
A consumer group collected information on HDTVs. They created a linear model to estimate the cost of an HDTV (in $) based on the screen size (in inches). Which is the most likely value of the slope of the line of best fit?

a. 0.70
b. 7
c. 70
d. 700
e. 7000

c. 70
The correlation between a family’s weekly income and the amount they spend on restaurant meals is found to be r=.30. Which must be true?

I. Families tend to spend about 30% of their incomes in restaurants
II. In general, the higher the income, the more families spend in restaurants
III. The line of best fit passes through 30% of the (income, restaurant$) data points

a. I only
b. II only
c. III only
d. II and III only
e. I, II, and III

b. II only
A regression analysis of company profits and the amount of money the company spent on advertising found r^2 = 0.72. Which of these is true?
I. This model can correctly predict the profit for 72% of companies
II. On average, about 72% of a company’s profit results from advertising
III. On average, companies spend about 72% of their profits on advertising

a. None
b. I only
c. II only
d. III only
e. I and III

c. II only
A medical researcher finds that the more overweight a person is, the higher his pulse rate tends to be. In fact, the model suggests that 12-pound differences in weight are associated with differences in pulse rate of 4 beats per minute. Which is true?

I. The correlation between pulse rate and weight is 0.33
II. If you lose 6 pounds your pulse rate will slow down 2 beats per minute
III. a positive residual means a person’s pulse rate is higher than he model predicts

a. none
b. I only
c. II only
d. III only
e. II and III only

d. III only
School administrators collect data on students attending the school. Which of the following variables is quantitative?

a. class (freshman, sophomore, junior, senior)
b. whether the student is in AP classes
c. grade point average
d. whether the student has taken the SAT
e. none of these

c. grade point average
Which of the following variables would most likely follow a Normal model?

a. family income
b. heights of singers in a co-ed choir
c. weights of adult male elephants
d. scores on an easy test
e. all of these

c. weights of adult male elephants
A professor has kept records on grades that students have earned in his class. If he wants to examine the percentage of students earning the grades A, B, C, D, and F during the most recent term, which kind of plot could he make?

a. boxplot
b. timeplot
c. dotplot
d. pie chart
e. histogram

d. pie chart
Two sections of a class took the same quiz. Section A had 15 students who had a mean score of 80, and Section B had 20 students who had a mean score of 90. Overall, what was the approximate mean score for all of the students on the quiz?

a. 84.3
b. 85.0
c. 85.7
d. none of these
e. cannot be determined

c. 85.7
Your Stats teacher tells you your test score was the 3rd quartile for the class. Which is true?

I. You got 75% on the test
II. You can’t really tell what this means without knowing the standard deviation
III. You can’t really tell what this means unless the class distribution is nearly Normal

a. none of these
b. I only
c. II only
d. III only
e. II and III

a. none of these
Suppose that a Normal model described student scores in a history class. Parker has a standardized score (z-score) of +2.5 This means that Parker

a. is 2.5 points above average for the class
b. is 2.5 standard deviations above average for the class
c. has a standard deviation of 2.5
d. has a sore that is 2.5 times the average for the class
e none of the above

b. is 2.5 standard deviations above average for the class
The advantage of making a stem-and-leaf display instead of a dotplot is that a stem-and-leaf display

a. satisfies the area principle
b. shows the shape of the distribution better than a dotplot
c. preserves the individual date values
d. a stem-and-leaf plot is for quantitative data, while a dotplot shows categorical data
e. none of these

c. preserves the individual data values
Which of the following summaries are changed by adding a constant to each data value?

I. the mean
II. the median
III. the standard deviation

a. I only
b. III only
c. I and II
d. I and III
e. I, II, and III

c. I and II
All but one of these statements contain a mistake. Which could be true?

a. the correlation between a football player’s weight and the position he plays is 0.54
b. the correlation between the amount of fertilizer used and the yield of beans is 0.42
c. the correlation between a car’s length and its fuel efficiency is 0.71 miles per gallon
d. there is a high correlation (1.09) between height of a corn stalk and its age in weeks
e. There is a correlation of 0.63 between gender and political party

b. the correlation between the amount of fertilizer used and the yield of beans is 0.42
Residuals are….

a. possible models not explore by the researcher
b. variation in the data that is explained by the model
c. the difference between observed responses and values predicted by the model
d. data collected from individuals that is not consistent with the rest of the group
e. none of these

c. the difference between observed responses and values predicted by the model
Which statement about influential points is true?

I. Removal of an influential point changes the regression line
II. Data points that are outliers in the horizontal direction are more likely to be influential than points that are outliers in the vertical directions
III. Influential points have large residuals

a. I only
b. I and II
c. I and III
d. II and III
e. I, II, and III

b. I and II
Which is true?

I. Random scatter in the residuals indicates a model with high predictive power
II. If two variables are very strongly associated, then the correlation between them will be near +1.0 or -1.0
III. The higher the correlation between two variables the more likely the association is based in cause and effect

a. none
b. I only
c. II only
d. I and II only
e. I, II, and III

a. none
A company’s sales increase by the same amount each year. This growth is…

a. linear
b. exponential
c. logarithmic
d. power
e. quadratic

a. linear
A company’s sales increase by the same percent each year. This growth is…

a. linear
b. exponential
c. logarithmic
d. power
e. quadratic

b. exponential
A scatterplot of 1/y^1/2 vs. x shows a strong positive linear pattern. It is probably true that

a. the correlation between X and Y is near +1.0
b. the scatterplot of Y vs X also shows a linear pattern
c. the residuals plot for regression of Y on X shows a curved pattern
d. large values of X are associated with large values of Y
e. accurate predictions can be made for Y even if extrapolation is involved

c. the residuals plot for regression of Y on X shows a curved pattern
It’s easy to measure the circumference of a tree’s trunk, but not so easy to measure its height. Foresters developed a model for ponderosa pines that they use to predict the tree’s height (in feet) from the circumference of its trunk (in inches): ln(h) = -1.2 + 1.4(ln C). A lumberjack finds a tree with a circumference of 60″; how tall does this model estimate the tree to be?

a. 5′
b. 11′
c. 19′
d. 83′
e. 93′

e. 93′
Two variables that are actually not related to each other may nonetheless have a very high correlation because they both result from some other, possibly hidden, factor. This is an example of

a. leverage
b. a lurking variable
c. extrapolation
d. regression
e. an outlier

b. a lurking variable
In an AP Stats class, 57% of students eat breakfast in the morning and 80% of students floss their teeth. Forty-six percent of students eat breakfast and also floss their teeth. What is the probability that a student from this class eats breakfast but does not floss their teeth?

a. 9%
b. 11%
c. 34%
d. 57%
e. 91%

b. 11%
In an AP Stats class, 57% of students eat breakfast in the morning and 80% of students floss their teeth. Forty-six percent of students eat breakfast and also floss their teeth. What is the probability that a student from this class eats breakfast or flosses their teeth?

a. 9%
b. 11%
c. 34%
d. 57%
e. 91%

e. 91%
Five juniors and four seniors have applied for two open student council positions. School administrators have decided to pick the two new members randomly. What is the probability they are both juniors or both seniors?

a. 0.395
b. 0.444
c. 0.506
d. 0.569
e. 0.722

b. 0.444
A fair coin has come up “heads” 10 times in a row. The probability that the coin will come up heads on the next flip is

a. less than 50%, since “tails” is due to come up
b. 50%
c. greater than 50%, since it appears that we are in a streak of “heads”
d. it cannot be determined

b. 50% (Law of Averages DOES NOT EXIST)
According to the National Telecommunication and Information Administration, 56.5% of U.S. households owned a computer in 2001. What is the probability that of three randomly selected U.S. households at least one owned a computer in 2001?

a. 18.0%
b. 43.5%
c. 56.5%
d. 82.0%
e. 91.8%

e. 91.8%
According to the National Telecommunication and Information Administration, 50.5% of U.S. households had Internet access in 2001. What is the probability that four randomly selected U.S. households all had Internet access in 2001?

a. 6.5%
b. 12.6%
c. 49.5%
d. 50.5%
e. 93.5%

a. 6.5%
Which of these has a Binomial model?

a. the number of people we survey until we find someone who has taken Statistics
b. the number of people we survey until we find two people who have taken statistics
c. the number of people in a class of 25 who have taken Statistics
d.the number of aces in a five-card Poker hand
e. the number of sodas students drink per day

c. the number of people in a class of 25 who have taken Statistics
Which of these has a Geometric model?

a. the number of people we survey until we find someone who has taken Statistics
b. the number of people we survey until we find two people who have taken statistics
c. the number of people in a class of 25 who have taken Statistics
d.the number of aces in a five-card Poker hand
e. the number of sodas students drink per day

a. the number of people we survey until we find someone who has taken Statistics
Batco, a company that sells batteries, claims that 99.5% of their batteries are in working order. how many would you expect to buy, on average, to find one that does not work?

a. 5
b. 100
c. 200
d. 995
e. 2000

c. 200 (do not work=success=p=.05)
Some marathons allow two runners to “split” marathons by each running a half marathon. Alice and Sharon plan to split a marathon. Alice’s half-marathon times average 92 minutes with a standard deviation of 4 minutes, and Sharon’s half-marathon times average 96 minutes with a standard deviation of 2 minutes. Assume that the women’s half-marathon times are independent. The expected time for Alice and Shaorn to complete a full marathon is 92+96=188 minutes. What is the standard deviation of their total time?

a. 2 minutes
b. 4.5 minutes
c. 6 minutes
d. 20 minutes
e. it cannot be determined

b. 4.5 minutes