Download AP Statistics Midterm Exam - Granite Bay High School / Granite Bay

Mid Rev--Pre Test Midterm Ch. 1-8
AP STATS
Name_________________________
Date____________Per_______
1. What is the difference between an observational study and well designed experiment?
2. A high school statistics class wants to conduct a survey to determine what percentage of
students in the school would be willing to pay a fee for participation in after-school activities.
They assign every student a number and use the random number generator on the calculator
to select 20 students. This plan is an example of which type of sampling?
a.
b.
c.
d.
e.
Cluster
Convenience
Simple random
Stratified random
Systematic
3. A new medication has been developed to treat sleep-onset insomnia (difficulty in falling
asleep). Researchers want to compare this drug to a drug that has been used in the past by
comparing the length of time it takes subjects to fall asleep. Of the following, which is the
best method for obtaining this information?
a. Randomly assign the subjects to two groups, giving the new drug to one group and the
old drug to the other group, then compare the results.
b. Have subjects choose which drug they are willing to use, the compare the results.
c. Assign the two drugs to the subjects on the basis of their past sleep history without
randomization, then compare the results.
d. Give the new drug to all subjects on the first night. Give the old drug to all subjects on
the second night. Compare the results.
e. Randomly assign the subjects to two groups, giving the new drug to one group and no
drug to the other group, then compare the results.
4. In which of the following situations would you not be able to use a census?
a. To determine what proportion of licensed bicycles on a university campus are mountain
bikes
b. To determine what proportion of students in high school support the beach volleyball
club
c. To determine what proportion of deer in the Tahoe forest are bucks
d. To determine what proportion of registered students enrolled in college live with their
parents
e. To determine what proportion of single-family dwellings in small town have patio
covers
5. Which of the following is a characteristic of stratified random sampling?
a. Convenience sampling is part of the sampling procedure
b. The population is divided into groups of units that are heterogenous on some
characteristic
c. The strata are not based on facts known before the sample is selected.
d. Each individual member of the population belongs to one and only one of the strata.
e. Every possible subset of the population, of the desired sample size, has an equal chance
of being selected.
6. Automobile brake pads are either metallic or nonmetallic. An experiment is to be conducted
to determine whether the stopping distance is the same for both types of brake pads. In
previous studies, it was determined that car size (small, medium, large) is associated with
stopping distance, but car type (sedan, wagon, coupe) is not associated with stopping
distance. This experiment would best be done
a. without blocking
b. by blocking on car size
c. by blocking on car type
d. by blocking on stopping distance
e. by blocking on brake pad type
7. Use the following boxplot to answer the following
300
I.
II.
III.
400
500
550
600
The 75th percentile rank is 400
The mean score is 500
The interquartile range is 300
a. I only
b. II only
c. III only
d. II and III
e. None are true
8. A group of students has 60 houseflies in a large container and needs to assign 20 to each of three
groups labeled A, B, C for an experiment. They can capture the flies one at a time when the flies
enter a side chamber in the container that is baited with food. Which of the following methods will
be most likely to result in three comparable groups of 20 houseflies each?
a. When each fly is caught, roll a die. If the die shows a 1 or 2, the fly is labeled A. If the die
shows a 3 or 4, the fly is labeled B. If the die shows a 5 or 6, the fly is labeled C. Repeat this
process for all 60 flies.
b. When each fly is caught, roll a die. If the die shows and even number, the fly is labeled A. If the
die shows an odd number, the fly is labeled B. When 20 flies have been labeled A and 20 flies
have been labeled B, the remaining flies are then labeled C.
c. Label the first 20 flies caught as group A, the second 20 as group B, and the third 20 caught as
group C.
d. Write the letters A, B, C on separate slips of paper. Randomly pick one of the slips of paper and
assign the first 20 flies caught to that group. Pick another slip and assign the next 20 flies caught
to that group. Assign the remaining flies to the remaining group.
e. Place each fly in its own numbered container (numbered from 1 to 60) in the order that it was
caught. Write the numbers from 1 to 60 on slips of paper, put the slips in a jar, and mix them
well. Pick 20 numbers out of the jar. Assign the flies in the containers with those numbers to
group A. Pick 20 more numbers and assign the flies in the containers with those numbers to
group B. Assign the remaining 20 flies to group C.
9. Consider the following two histograms, then decide which of the statements are false.
a.
b.
c.
d.
e.
100
120
100
120
140
140
160
180
160
180
Both sets are symmetric
They have different means and ranges
They do not have the same variance
They do not have the same standard deviation
Only one set has gaps and clusters
10. Which of the following statements about comparative bar charts are true?
I. A comparative bar chart can be used for only for numerical data.
II. A comparative bar chart works best for small number of observations.
III. The vertical axis of a comparative bar chart is always relative frequency.
11. Which of the following can a stem-and-leaf plot display?
I. gaps in the data
II. potential outliers
III. symmetry
12. Which of the following statements about histograms are true?
I. The upper limit of a class interval corresponds to less than, while the lower limit
corresponds to greater than or equal to.
II. The bars of each class interval need not share a side with adjacent class interval bars.
III. Relative frequency histograms and frequency histograms have the same shape and
proportions.
13. When a set of data has suspect outliers, which of the following are preferred measures of
central tendency?
a.
b.
c.
d.
e.
mean and variance
mean and range
median and interquartile range
median and range
mean and standard deviation
14. The following double bar graphs shows the choice of heating fuel for new homes
completed during the indicated years. In each pair the top bar indicates electricity while
the lower bar indicates gas.
34%
1989
58%
33%
1990
59%
32%
1991
60%
29%
1992
65%
29%
1993
66%
Which of the following are false statements?
I. The percentage of new homes using fuels other than electricity and gas has stayed the
same from one year to another.
II. The percentage of new homes using electricity has never risen from one year to
another.
III. The percentage of new homes using gas has increased every year.
a.
b.
c.
d.
e.
I
II
III
I, II, and III
None of the above gives the complete set of true responses.
15. If quartiles Q1  30 and Q3  50 , which of the following must be true?
I.
II.
III.
a.
b.
c.
d.
e.
The standard deviation is at most 10.
The mean is 40.
The median is between 30 and 50.
I only
II only
III only
All are true.
None are true.
16. The stem plot below displays the weights (in ounces) of a random sample of tomatoes
grown on a local farm.
Weights of Tomatoes (oz)
2L
4
2H
3L
2
3H
8 9
4L
1 3
4H
5 5 8 9
5L
1 1 1 2 2 3 3 4
5H
6 6 8 9 9 9
6L
2 2 3 3 4 4
6H
5 5 5 6
stem: ones
leaf: tenths
Which of the following are false statements based on the display?
I.
II.
III.
The range of the data is 4.2 ounces.
The tomato data is negatively skewed .
A typical tomato weighs about 4 ounces.
a. I
c.
III
b. II
d.
I, II, and III
e. None of the above gives the complete set of true responses.
17. Which of the following are false statements?
I.
II.
III.
a.
b.
c.
d.
e
While the range is not affected by outliers, the interquartile range is.
The range of the sample data set is never greater than the range of the population.
The interquartile range is half the distance between the first quartile and the third
quartile.
I only
II only
III only
I and II
I and III
18. Suppose the average score on a national test is 800 with a standard deviation of 50. If each
score is increased by 25, what are the new mean and standard deviation?
19. Suppose the average score on a national test is 800 with a standard deviation of 50. If each
score is increased by 25%, what are the new mean and standard deviation?
20. A 1995 poll by the Program for International Policy asked respondents what percentage of
the U.S. budget they thought went to foreign aid. The mean response was 12%, and the
median was 17%. (The actual amount is less than 1%.) What do these responses indicate
about the likely shape of the distribution of all responses?
a.
b.
c.
d.
e.
The distribution is uniform between 12% and 17%.
The distribution is skewed to the left.
The distribution is symmetric around 14.5%.
The distribution is skewed to the right.
The distribution is bell-shaped with a standard deviation of 2.5%.
21. Assuming that batting averages have a bell-shaped distribution, arrange in descending order:
I.
II.
III.
a.
b.
c.
d.
e.
An average at the first quartile, Q1 .
An average with a z-score of -1.
An average with a percentile rank of 20%.
I, II, III
I, III, II
II, I, III
II, III, I
III, II, I
22. Which of the following are false statements?
I.
II.
III.
a.
b.
c.
d.
e.
If the sample has variance zero, the sample mean and the sample median are equal.
If the sample has variance zero, the variance of the population is also zero.
If the population has variance zero, the variance of the sample is also zero.
I and II
I and III
II only
I, II, and III
None of the above gives the complete set of true responses.
23. A stemplot for the 1988 per capita personal income for the 50 states is
11
12
13
14
15
16
17
18
19
20
21
22
0, 7
0, 2, 2, 5, 5, 6, 7, 7, 7, 8, 8
3, 7, 7
1, 6, 7, 8, 9
0, 0, 0, 2, 4, 4, 5, 5, 9
2, 4, 4, 5, 6, 8, 8, 9
4, 6, 6, 7
9
0, 3, 3, 5
7
9
8
Which of the following best describes these data?
a.
Symmetric distribution with outliers on high end
b.
Symmetric distribution, median greater than mean
c.
Symmetric distribution, mean greater than median
d.
Skewed distribution, median greater than mean
e.
Skewed distribution, mean greater than median
Stem: thousands
Leaf: hundreds
24. Which of the following statements are true?
I.
II.
III.
If a distribution is skewed to the right, its median is often greater than its mean.
If the right and left sides of a histogram are mirror images of each other, the
distribution is symmetric.
A distribution spread far to the left is said to be skewed to the left.
a.
b.
c.
d.
e.
II only
I and II
I and III
II and III
None of the above gives the complete set of true responses.
25. The following graph shows the cumulative proportions with regards to outstanding balances
on credit cards.
1.0
Cumulative
Proportion
What is the approximate value of the
median?
0.8
0.6
a.
b.
c.
0.4
0.2
$500
$800
$2000
d.
e.
$2500
$4000
1000 2000 3000 4000
26. A correlation and regression analysis reveals that r = 0.72 and r2 = 0.53 when 60 pairs of
observations, (x,y) are considered. Therefore, we can conclude that
a.
b.
c.
d.
x causes y to occur
there is a strong nonlinear relationship between x and y
there is a moderate linear relationship between x and y
there is a strong linear relationship between x and y
27. A least squares regression line was fitted to the weights (in pounds) versus age (in months) of
a group of many young children. The equation on the line is yˆ  15.52  0.34 x where ŷ is
the predicted weight and x is the age of the child. A 23 month old child in this group has an
actual weight of 28 pounds. What is the residual weight, in pounds, for this child?
28. A delivery service places packages into large containers before flying them across the country. These
filled containers vary greatly in their weight. Suppose the delivery service’s airplanes always
transports two such containers on each flight. The two containers are chosen so their combined
weight is close to, but does not exceed, a specified weight limit. A random sample of flights with
these containers is taken, and the weight of each of the two containers on each selected flight is
recorded. The weights of the two containers on the same flight
a.
b.
c.
d.
e.
will have a correlation of 1
will have a correlation of 0
will have a positive correlation that is less than 1
will have a negative correlation
cannot be determined from the information given
29. The graphs of the sampling distributions, I and II, of the sample mean of the same random
variable for samples of two different sizes are shown above. Which of the following
statements must be true about the sample size of distribution I?
a.
b.
c.
d.
e.
The sample sizes cannot be compared based on theses graphs.
The sample size of I is equal to the sample size of II.
The sample size of I is less than the sample size of II.
The sample size of I is greater than the sample size of II.
The sample size does not affect the sampling distribution.
30. The linear correlation coefficient was reported to equal -1. Which of the following is not
true?
a.
b.
c.
d.
A computation error was made in computing r.
The two variables are negatively correlated.
All of the sample data points fall along a straight line that has a negative slope.
The coefficient of determination equals 100%.
31. If the slope of the regression line is negative and the coefficient of determination is .81, then
find Pearson’s correlation coefficient
32. Two measures x and y were taken on 18 subjects. The first of two regressions, Regression I,
yielded yˆ  24.5  16.1x and had the following residual plot.
The second regression, Regression II, yielded log y  1.6  0.51log x and had the following
residual plot.
Which of the following conclusions is best supported by the evidence above?
a.
b.
c.
d.
e.
There is a nonlinear relationship between x and y, and Regression I yields a better fit.
There is a nonlinear relationship between x and y, and Regression II yields a better fit.
There is a negative correlation between x and y.
There is a linear relationship between x and y, and Regression I yields a better fit.
There is a linear relationship between x and y, and Regression II yields a better fit.
33. In a study of the performance of a computer printer, the size (in kilobytes) and the printing
time (in seconds) for each of 22 small text files were recorded. A regression line was a
satisfactory description of the relationship between size and printing time. The results of the
regression analysis are shown below.
Which of the following statements are true?
I.
There’s a strong positive linear correlation since the correlation coefficient is .935
II.
The regression equation is y= 3.47812 + 11.6559x
III.
The regression equation is y=11.6599 + 3.47812x
a. Only I
b. Only II
c. Only III
d. I and III
e. none of the responses are correct
34. Dennis is planning to fly from New York to Los Angeles and will take the Airtight Airlines
flight that leaves at 8 A.M. The Web site he used to make his reservation states that the
probability that the flight will arrive in Los Angeles on time is 0.60. Of the following, which
is the most reasonable explanation for how that probability could have been estimated?
a. From the fact that, of all airline flights in the United States, 60% arrive on time
b. From the fact that, on all previous days this particular flight had been scheduled, it had
arrived on time 60% of those days
c. By using an extended weather forecast for the date of her flight, which showed a 40%
chance of bad weather
d. By making assumptions about how airplanes work, and factoring all of those assumptions
into an equation to arrive at the probability
e. From the fact that, of all airline flights arriving in California, 60% arrive on time
35. Vaughn interviewed 100 people and classified them according to their attitude toward small
cars and their personality type. The results are shown in the table below.
Attitude
Toward
Small Cars
Positive
Neutral
Negative
Total
Personality Type
Type A
Type B
25
12
11
9
24
19
60
40
Total
37
20
43
100
Which of the following is true?
a. The proportion that has a positive attitude toward small cars is higher among people with
a type B personality type than among people with a type A personality type.
b. More than half of the 100 respondents have a type A personality type and a positive
attitude toward small cars.
c. Of the three attitude groups, the group with the negative attitude has the highest
proportion of type A personality types.
d. Of the three attitude groups, the group with the neutral attitude has the highest proportion
of type B personality types.
e. For each personality type, more than half of the 100 respondents have a neutral attitude
toward small cars.
36. An experiment has three mutually exclusive outcomes, A, B, and C. If P(A) = 0.15, P(B) =
0.60, and P(C) = 0.25, which of the following must be true?
I.
II.
III.
P(A or C) = P(A) + P(C)
B and C are independent.
P(A and C) = 0
a.
b.
I only
I and II only
c.
d.
I and III only
II and III only
e.
I, II, and III
37. Suppose that 40 percent of the subscribers to a cable television service watch the shopping channel at
least once a week. You are to design a simulation to estimate the probability that none of the five
randomly selected subscribers watches the shopping channel at least once a week. Which of the
following assignment’s of the digits 0 through 9 would be appropriate for modeling an individual
subscriber’s behavior in this simulation?
a.
b.
c.
Assign “0” as watching the shopping channel at least once a week and “1, 2, 3, 4, and 5” as not watching;
ignore digits “6, 7, 8, and 9.”
Assign “0, 1, 2, 3” as watching the shopping channel at least once a week and “4, 5, 6, 7, 8, and 9” as not
watching.
Assign “0, 1, 2, 3, 4” as watching the shopping channel at least once a week and “ 5, 6, 7, 8, and 9” as not
watching.
d.
Assign “0, 1, 2, 3, 4, 5” as watching the shopping channel at least once a week and “6, 7, 8, and 9” as not
watching.
e.
Assign “4” as watching the shopping channel at least once a week and “0, 1, 2, 3, 5, 6, 7, 8, and 9” as not
watching.”
38. 80% percent of the people who have a particular disease will have a positive result on a
given diagnostic test. 85% percent of the people who do not have the disease will have a
negative result on this test. Suppose 7% of the population has the disease. Given a person
tested positive, what is the probability that they do not have the disease?
39. An urn contains exactly three balls numbered 1, 2, and 3 respectively. Random samples of
two balls are drawn from the urn with replacement. The average,
x-bar = (x1 + x2)/2, where x1 and x2 are the numbers on the selected balls, is recorded after
each drawing. Which of the following describes the sampling distribution of x-bar?
40. Traffic data revealed that 35 percent of automobiles traveling along a portion of an interstate
highway were exceeding the legal speed limit. Using highway cameras and license plate
registration, it was also determined that 52 percent of sports cars were also speeding along
the same portion of the highway. What is the probability that a randomly selected car along
the same portion of the highway was a speeding sports car?
a.
b.
c.
d.
e.
0.870
0.673
0.182
0.170
It cannot be determined from the information given.
41. Which of the followings are discrete?
I. Digital watch readings
II. The body temperature of a walrus.
III. The number of shoes in a factory.
a.
b.
c.
d.
III only
II and III only
I, II, and III
I and III only
42. The number of points, X, scored in a game has the probability distribution below,
The number of points obtained in one game is independent of the number of points obtained
in a second game. When the game is played twice, the sum of the number of points for both
times could be 0, 1, 2, 3, or 4. If Y represents the sampling distribution of the sum of the
scores when the game is played twice, for which value of Y will the probability be the
greatest?
a. 0
d. 3
b. 1
e. 4
c.
2
43. The probability of being a 2nd grader in a public school in Placer County is .80. If three 2nd
graders are independent and randomly selected, what is the probability that the first one is
from a private school and the next two are from a public school?
44. The probability of adults liking Giants Orange is .75. If 7 adults are randomly selected, what
is the probability that 4 like Giants Orange?
45. Given the probability distribution, find the mean and standard deviation.
X
0
P(x) .40
1
.31
2
.15
3
.08
4
.06
46. 60% of grocery stores have Cinnamon Cheerios. If Brandon needs to go from store to store
until he finds Cinnamon Cheerios, what is the probability he will find it on exactly the fourth
store, if he stops looking when he finds it?
47. The mean bowling score for Kiah is 123 with a  X of 5.6.What is the mean bowling score
which separates the top 30% from the rest?
48. The mean length between elbow and wrists is 15.0” with a standard deviation of 2.6”. Find
the probability of having such a length < 14.2” from a sample of 40 people.
49. The probability of an AP Statistics student taking the AP test is .96. If a random sample of
300 students is taken, find the probability that (.93 < p̂ < .99)
Answers:
1. In an experiment, you intentionally force a treatment on the subjects.
2. C
3. A
4. C
5. D
6. B
7. E
8. E
9. B
10. none
11. I,II,III
12. I,III
13. C
14. A
15. C
16. C
17. E
18. 825,50
19. 1000,62.5
20. B
21. B
22. C
23. E
24. D
25 B
26. C
27. 4.66
28. D
29. D
30. A
31. -.9
32. B
33. D
34. B
35. D
36. C
37. B
38. .7136
39. B
40. E
41. D
42. C
43. .128
44. .173
45. 1.09,1.18 46. .0384
47. 125.94
48. .0258
49. .9919