Final Exam Review
Name:
On July 15, 2004, the Harris Poll released the results of a study asking whether people
favored or opposed abolishing the penny. Of a national sample of 2136 adults, 59%
opposed abolishing the penny.
1.
Which of the following is a categorical variable in the Harris Poll?
(a) the 2004 participants
(b) whether each person favors or opposes abolishing the penny.
(c) whether or not a person responded to the poll
(d) the percent of people who oppose abolishing the penny
2.
What are the observational units (individuals) in the study?
(a) the number of people who would abolish the penny in the entire population
(b) the number of people who would abolish the penny in the sample
(c) the people who responded to the poll
(d) the percent of people who oppose abolishing the penny
3.
Suppose that the observational units (individuals) in a study are Pennsylvania
high schools. Which of the following is not a valid variable?
(a.) whether or not the school has an animal for its mascot
(b.) proportion of students scoring proficient or better on the PSSA at each school
(c.) total number of students at each school
(d.) number of high schools in Pennsylvania which have indoor pools
4.
Suppose that 80% of all American students send a card to their mother on
Mother's Day and that you selected a simple random sample of 400 American
college students and to determine the proportion of them who send a card to
their mother on Mother's Day. Suppose further that in the random sample of
400 students, 300 or 75% of them send a card to their mothers.
(a.)
(b.)
(c.)
(d.)
80% is a parameter, 75% is a statistic.
75% is a parameter, 80% is a statistic.
Both 75% and 80% represent statistics.
Both 75% and 80% represent parameters.
5.
A sample is:
(a.) a number resulting from the manipulation of raw data according to specified
rules.
(b.) a subset of a population.
(c.) a characteristic of a population which is measurable.
(d.) a complete set of individuals, objects, or measurements having some
common observable characteristic.
For questions 6 and 7 use the following situation:
Suppose that 80% of all American college students send a card to their mother on
Mother's Day and that you selected a simple random sample of 400 American
college students and to determine the proportion of them who send a card to
their mother on Mother's Day. Suppose further that in the random sample of
400 students, 300 or 75% of them send a card to their mothers.
6.
Which of the following is true?
(a.) the 400 college students are the population
(b.) the sample size is 400
(c.)
all college students in the world are the sample
(d.) the sample is the 300 students who send a card
7.
Which of the following is the parameter of interest?
(a.) the proportion of American college students who send a card on Mother’s
Day
(b.) the proportion of the 400 students in the sample who send a card
(c.)
the proportion of all college students in the world who send a card
(d.) the 300 students in the sample who sent a card
Below is a list of names numbered 1 to 20. Use the random number table to randomly
select 5 names from the list by starting at the beginning of the table and taking pairs of
digits.
1
2
3
4
5
6
7
8
9
10
Sofia
Eassa
Jeffrey
Shakoya
John
Rebecca
William
Johanna
Allyson
Brandon
11
12
13
14
15
16
17
18
19
20
Dara
Jay
Nicole
Francis
Audrey
Anthoula
Hiep
Sean
Shanira
Alexis
Table of random digits
11035 61298 32134 10012 99091
67743 11123 45672 04567 00998
8.
What is the second name selected?
(a.) Dara
(b.) Jeffrey
(c.) Jay
(d.) Allyson
9.
What is the fifth name selected?
(a.) Dara
(b.) Jeffrey
(c.) Jay
(d.) Allyson
10.
Which best describes a SRS?
(a.) Gives every member of the population an equal chance of being selected.
(b.) Gives every member of the sample an equal chance of being selected.
(c.) Gives every different sample size an equal chance of being selected.
(d.) Gives every different population an equal chance of being selected.
11.
You are concerned that your employees have little saved for retirement. You
conduct a survey of your 100,000 employees using a simple random sample of
size 47. You find that the mean of the savings of this sample of employees is
$40,000 with standard deviation of $3,000.
This is an example of an…
(a) observational study since subjects are randomly assigned to groups
(b) observational study since it is based on taking a sample of a population
without intervening
(c) experiment since subjects are randomly assigned to groups
(d) experiment study since it is based on taking a sample of a population without
intervening
12.
Researchers concerned about the effects of excessive television viewing on
students school performance are planning to conduct a study. Which of the
following is true?
(a.) This study would be considered an observational study if they assigned one
group of students to watch 4 hours of television each day and another group to
not watch any television.
(b.) This study would be considered biased if they assigned one group of students
to watch 4 hours of television each day and another group to not watch any TV.
(c.)This study would be considered an experiment if they assigned one group of
students to watch 4 hours of television each day and another group to not watch
any TV.
(d.) This study would be considered an experiment if they took a random sample
of students, recorded their grades and the number of hours of television they
watched.
13.
A survey is to be undertaken of recent nursing graduates in order to compare the
starting salaries of women and men. For each graduate, three variables are to be
recorded (among others) sex, starting salary, and area of specialization.
(a) Sex and starting salary are explanatory variables; area of specialization is a
response variable
(b) Sex is an explanatory variable; starting salary and area of specialization are
response variables.
(c) Sex is an explanatory variable; starting salary is a response variable; area of
specialization is a possible confounding variable
(d) Sex is a response variable; starting salary is an explanatory variable; area of
specialization is a possible confounding variable
(e) Sex and area of specialization are response variables; starting salary is an
explanatory variable.
14.
A study was conducted to see if Smartfood Popcorn makes people smarter. A
group of 50 participants in the study were divided into two groups. One group
received Smartfood Popcorn before taking a spelling test, and the other took the
test without first getting popcorn. The control group in an experiment should be
designed to receive:
(a.) the opposite of the experiences afforded the experimental group.
(b.) the experiences afforded the experimental group except for the treatment
under examination.
(c.) the experiences afforded the experimental group except for receiving the
treatment at random.
(d.) the experiences which constitute an absence of the experiences received by
the experimental group.
15.
The Smartfood experiment would be said to take into account the principle of
blindness if ___________, and it could be said to be double-blind if
_____________.
(a.) the subjects are randomly assigned to either eat Smartfood or not;
those evaluating the subjects are blindfolded
(b.) the subjects are not aware of which treatment group they are in;
those evaluating the subjects are not aware of which treatment group received
Smartfood
(c.) the subjects are selected at random from the population;
those evaluating the subjects are not aware of which treatment group the subjects
are in
(d.) the subjects are not aware of which treatment group they are in;
the two treatment groups are never come in contact
16.
An experiment is conducted to determine if the use of certain specified amounts
of a drug will increase the IQ scores for students in the fifth grade.
In this experiment, IQ serves as:
(a.) a response variable
(b.) an explanatory variable
(c.) a placebo variable
(d.) a control variable
17.
A new headache remedy was given to a group of 25 subjects who had headaches.
Four hours after taking the new remedy, 20 of the subjects reported that their
headaches had disappeared. From this information you should conclude:
(a) that the remedy is effective for the treatment of headaches.
(b) nothing, because the sample size is too small.
(c) nothing, because there is no control group for comparison.
(d) that the new treatment is better than aspirin.
18.
Which of the flowing is NOT a reason that subjects should be assigned to
treatments at random?
(a) to get a random sample of the population of interest
(b) to eliminate the potential for researchers to influence the results
(c) to create experimental groups that are similar
(d) so that the effects of variable that were not measured will likely be balanced
out between the experimental groups
19.
Researchers have observed that drinking red wine seems to lead to fewer men
having heart attacks. More recently, others have noted that drinking red wine
leads to headaches and people with headaches tend to take aspirin.
Furthermore, aspirin is known to reduce the changes of having heart attacks.
Given these facts, the relationship between drinking red wine and having heart
attacks would be best described as being due to:
(a.) cause-and-effect.
(b.) strong correlation.
(c.) a lurking variable.
(d.) placebo effect.
20.
There is a relationship between the number of drownings and ice
cream sales. This is an example of an association likely caused by:
(a) coincidence
(b) the fact that ice cream causes drownings
(c) confounding or lurking variable
(d) the fact that drowning cause eating ice cream
21.
An experiment was designed to investigate the effect of the amount of water and
seed variety upon subsequent growth of plants. Each plant was potted in a clay
plot, and a measured amount of water was given weekly. The plants that were
assigned to receive more water had all been placed closer to a window that the
ones that received less water. The height of the plant at the end of the experiment
was measured. Which of the following is not correct?
(a) The response variable is the plant height.
(b) The explanatory variables are the amount of water and seed variety.
(c) The seeds should be randomly selected from the population of all seed
varieties rather than randomly assigned to receive more or less water.
(d) The effect of the amount of water was confounded by the effect of being near
the window
22.
Which of the following best describes an outlier?
(a) The largest or smallest number in a distribution
(b) An observation that doesn’t fit in with the overall pattern of variability
(c) Any really big number is an outlier
(d) An unusually tall peak in the distribution of a variable
23.
The histogram displays the percent of overweight adults in each state. Which of
the following is NOT true?
(a) The distribution is symmetric
(b) In a typical state about 37% of the
people are overweight
(c) 14 states have less than 36%
overweight
(d) 2 states have 11% overweight
The following side-by-side boxplots represent the rushing yards gained by the starting
running backs in the opening game. Compare and contrast their performance.
24.
Carson runs further than 5 yards about what percent of the time?
(a) 15%
(b) 25%
(c) 50%
(d) 75%
25.
_____ tends to run further. _____ is
more consistent.
(a) Asika; Asika
(b) Asika; Carson
(c) Carson; Asika
(d) Carson; Carson
26.
Based on the dotplots of February temperatures for three cities, answer the
following which of the following is
NOT true?
(a) San Luis Obispo experienced
generally higher temperatures than
Sedona and Lincoln
(b) The distribution of temperatures
for Sedona is skewed toward lower
values
(c) The city with the most consistent
temperatures was Sedona
(d) The temperatures in Lincoln tend to be higher than those in Sedona
27.
The measure of spread which is resistant to extreme scores on the higher or
lower end of a distribution is the:
(a) median.
(b) mean.
(c) standard deviation.
(d) IQR
28.
Making the largest number in a data set much larger will increase the ______
but not change the _________.
(a) median; mean
(b) mean; standard deviation
(c) standard deviation; IQR
(d) IQR; median
29.
Which of the following is not a measure of center?
(a.) mean
(b.) median
(c.) mode
(d.) standard deviation
30.
The dotplot to the right compares some
systolic and diastolic blood pressure
measurements. Which of the following is
NOT true?
(a.) systolic blood pressure tends to be
higher than diastolic blood pressure
(b.) systolic blood pressure reading
tend to be above 100
(c.) every systolic reading is higher than
every diastolic reading
(d.) diastolic blood pressure readings
tend to be below 100
31.
If you are told a population has a mean of 25 and a standard deviation of 0, what
must you conclude?
(a.) Someone has made a mistake.
(b.) There is only one element in the population.
(c.) There are no elements in the population.
(d.) All the elements in the population are 25.
32.
Calculate the range and the IQR for the data set: {1,2,3,4,5,6,7,8}
(a.) 7 and 4
(b.) 8 and 3
(c.) 8 and 1
(d.) 6 and 5
33.
According to the empirical rule, for any mound-shaped distribution, about 95%
of the data will be…
(a) within one standard deviation of the mean
(b) within two standard deviations of the mean
(c) within three standard deviations of the mean
(d) within four standard deviation of the mean
34.
If the mean of a distribution of test score is 70 and the standard deviation is 10,
the empirical rule predicts that about 68% of the students scored between…
(a) 60 and 80
(b) 70 and 80
(c) 50 and 90
(d) 60 and 90
Consider the following two-way table showing the favorite leisure activities for 50
adults.
Dance Sports TV Total
Men
2
10
8
20
Women
16
6
8
30
Total
18
16
16
50
35. What proportion of people preferring Dance are woman and what proportion are
men?
(a.)
(b.)
(c.)
(d.)
89%, 11%
40%, 60%
36%, 64%
50%, 50%
36. What is the conditional distribution of the variable Gender for people preferring
TV?
(a.)
(b.)
(c.)
(d.)
89%, 11%
40%, 60%
36%, 64%
50%, 50%
37. What is the marginal distribution of the variable Gender?
(a.)
(b.)
(c.)
(d.)
89%, 11%
40%, 60%
36%, 64%
50%, 50%
Consider the two-way table below based on a class of 30 students and their responses as
to whether or not they own a cat and whether or not they own a dog:
38.
Has a Cat
No Cat
Total
Has a Dog
8
4
12
No Dog
2
16
18
Total
10
20
30
Describe the relationship between having a cat and having a dog in this class.
(a.) whether a student has a dog is not related to whether the student has a cat
(b.) Students with a cat are more likely to also have a dog than students without a
cat
(c.) Students with a dog are less likely to have a cat than students who do not
have a dog
(d.) Most students have either a cat or a dog or both
39.
The following is a scatterplot displays SAT math scores for each state versus the
percent of students taking the exam.
Which best describes the relationship?
(a.) positive, strong, linear
(b.) negative, moderate, linear
(c.)
negative, strong, non linear
(d.) no relationship
40.
The correlation between the Governor’s salary in each state and the median home
value in the state is positive. Therefore, we can conclude that…
(a.)
(b.)
(c.)
(d.)
states with above average Governor’s salaries tend to have below average
home values.
states with below average Governor’s salaries tend to have above average
home values.
states with above average Governor’s salaries tend to have above average
home values.
there is no relationship between housing values and salaries of Governors.
41.
Which of the following is true about correlation?
(a.) it is only appropriate to use correlation when the relationship is linear
(b.) if the correlation coefficient is close to 1 or -1, there is a cause-and-effect
relationship
(c.)
correlation is resistant to outliers
(d.) all of the above are true
42.
If a correlation coefficient between Age and Coolness Rating is -0.70, then:
(a) A person’s Age is usually less than the person’s Coolness Rating.
(b) A person’s Age is usually more than the person’s Coolness Rating.
(c) Below average Ages tend to be associated with below average values of
Coolness.
(d) Below average Ages tend to go with above average values of Coolness.
43.
Below is the Statcrunch output for a regression run on “Airfare” (in dollars)
versus “Distance” (in miles) for a set of data for flights between 12 cities.
Simple linear regression results:
Dependent Variable: Airfare
Independent Variable: Distance
Airfare = 83.26736 + 0.11737509 Distance
Sample size: 12
R (correlation coefficient) = 0.795
R-sq = 0.63200194
Estimate of error standard deviation: 37.827023
The slope of the regression equation indicates that…
(a)
There is a strong negative linear relationship
(b)
An additional mile tends to cost about 11.7 cents
(c)
A trip of 0 miles costs .117 dollars
(d)
None of the above
44.
The “line of best fit” under the least squares criterion is the one which…
(a)
minimizes the sum of all the perpendicular distances from the points to
the line.
(b)
has the greatest sum of squared errors in predictions.
(c)
has the smallest sum of squared residuals
(d)
has the smallest average residual
45.
Which is a correct interpretation of the Law of Large Numbers?
(a.) If you flip a coin 10 times and get 9 heads, we expect to get tails on the
next toss.
(b.) If you flip a coin a small number of times you are more likely to get close to
50% “heads” than if you flip a coin a large number of times.
(c.)
If you flip a coin twice and get “heads” both times, the next flip will most
likely come up “tails”
(d.) If you flip a coin 50 times, you probably won’t get exactly 25 “heads” but
you are likely to get somewhat close to 50% “heads”
46.
Which of the following is NOT a possible probability?
(a.) 25/100
(b.) 1.25
(c.) 1
(d.) 0
47.
When rolling a pair of 6-sided dice, what is the probability of rolling a sum of 6 or
7?
(a.) 1/6
(b.) 3/14
(c.) 5/12
(d.) 11/36
48.
Tina has 5 red, 6 blue, 3 white, and 4 orange marbles. All marbles are put in a
sack and one marble is selected at random. Compute the probability of drawing a
red marble and the probability of drawing a blue or white marble.
(a.) 4/19; 9/20
(b.) 3/10; 11/20
(c.) 5/18; 1/2
(d.) 9/21; 7/18
49.
In a basketball one-and-one situation. If a player makes the first foul shot, she
gets another foul shot. If she misses it , she does not get to shoot again. (So a
player can score 0,1, or 2 points in a one-and-one situation.) Suppose Liz has a
70% chance of making each foul shot. What is the probability that she scores
exactly one point in a one-and-one situation?
(a.) 70%
(b.) 9%
(c.) 49%
(d.) 21%
50.
A drawer contains 5 black socks and 3 blue socks. If you reach into the drawer
without looking and pull out two socks, what is the probability that you get a
matching pair?
(a.) 21/56
(b.) 13/28
(c.) 4/56
(d.) ½
51.
The binomial probability formula is P(X = k) = nCk × pk (1- p)n-k . Which of the
following sets of values when substituted into the formula above gives the
probability of getting 6 sixes in 10 rolls of a die?
(a) n = 4, p = 10, k = 1/6
(b) n = 10, p = 1/6, k = 4 none of these: n = 10, p =1/6, k = 6
(c) n = 10, p = 6, k = 1/6
(d) n = 4, p = 1/6, k = 10
52.
Which of the following is not a situation where the binomial probability formula
should be applied?
(a.)
(b.)
(c.)
(d.)
53.
A coin is flipped 20 times. What is the probability of getting 5 or more
heads?
What is the probability that the first 6 occurs on the 5th roll of a six-sided
die?
What is the probability that Liz will make exactly 3 out of 5 shots if she has
a 70% chance of making each shot and we assume independence?
A bag contains 6 marbles of which two are green. A marble is selected at
random from the bag, the color is noted, and the marble is returned to the
bag. Repeating this action 15 times, what is the probability of getting 5 or
fewer green marbles?
Compute the z-score for a score of 70 on a test with the following summary
statistics:
min = 20, Q1 =70, med = 75, Q3 = 76, max = 100, s = 4, x = 70
(a) z = 2
(b) z = 2.5
(c) z = 0
(d) z = 7
54.
A negative z-score indicates…
(a) that someone made a computational error
(b) that the mean is a negative number
(c) that the distribution is skewed toward lower values
(d) that the item in question is below the mean
55.
Suppose a medical experiment randomly assigns patients with a certain condition
to either receive an “old” treatment or a “new” treatment. The experimenters are
interested in whether the new treatment works better than the old treatment.
Which of the following would be an appropriate null hypothesis?
(a.)
(b.)
(c.)
(d.)
56.
The new treatment works better than the old treatment
The new treatment works the same as the old treatment
The old treatment works better than the new treatment
Neither the old or new treatments work.
In an experiment to study attempting to identify factors which can influence
people’s responses to survey questions, subjects were randomly given one of the
two following statements and asked whether they agree or disagree:
A: “Individuals are more to blame than social conditions for crime and
lawlessness in this country.”
B: “Social conditions are more responsible than individuals for crime and
lawlessness in this country.”
The responses are summarized below:
Blame Individuals Blame Social Conditions Total
A
282
191
473
B
204
268
472
Total
486
459
945
Statistic
Chi-square
DF
Value
1 25.4347 <0.0001
Which of the following is an appropriate conclusion for a chi-square test of the
null hypothesis that the wording of the question did not influence the responses:
(a.)
(b.)
(c.)
(d.)
P-value
Accept the null hypothesis. There isn’t sufficient evidence to demonstrate
that the wording of the question had an effect.
Reject the null hypothesis. There is strong evidence that people were
influenced by a tendency to agree with the researcher
Fail to reject the null hypothesis. People were more likely to disagree than
to agree with whichever statement was given.
Reject the alternative hypothesis. There no evidence suggesting that the
wording of the question influenced responses.
57.
Which of the following is the best explanation of a null hypothesis, Ho, in a
statistical test.
(a) a statement of what we are trying to prove in an experiment
(b) it is usually a statement that “there really is a difference”
(c) a neutral assumption made for the sake of argument that the researcher tries
to disprove based on conflict with the observed data
(d) it is the hypothesis that the data cannot be explained by random variability
58.
A p-value of 0.11 would indicate…
(a) that someone made a computational error
(b) strong evidence against the null hypothesis
(c) that the alternative hypothesis must be false
(d) that we should fail to reject the alternative hypothesis at a .05 significance
level
59.
Roberto suspects that his brother’s coin is biased towards heads. He flips the coin
a large number of times and records the results. Suppose that the number of
“heads” he got differs from the expected number of “heads” from a fair coin so
much that the p-value in a statistical test of significance is 0.04. Which of the
following is NOT a correct interpretation of this p-value?
(a) In only 4 random samples in one hundred would we see such a large
difference between the observed and expected numbers of heads when
flipping a fair coin
(b) The null hypothesis of the test is rejected at the .05 significance level
(c) The coin is biased such that it comes up “heads” less than 4% of the time.
(d) If Roberto’s brother’s coin is fair, the probability of observing such a large
difference between the observed and expected numbers of “heads” is fairly
small.
60.
It is appropriate to reject the null hypothesis in a test of significance if…
(a) it would be very unlikely to get the sort of data that was observed if the null
hypothesis were true.
(b) the data are consistent with what would be expected if the null hypothesis
were true
(c) the significance level is .05 and the p-value is greater than .05
(d) the value of the test statistic is close to 0
61.
Researchers would like to understand how pet ownership is related to longevity.
Which of the following is true?
(a.) This study would be considered an observational study if they randomly
assigned subjects to either receive a pet or not.
(b.) It would only be appropriate to conclude that there is a cause and effect
relationship based on the results of an experiment rather than an observational
study
(c.)This study would be considered an experiment if they took a random sample
of pet owners and noted whether or not they owned a pet
(d.) It is only possible to infer a cause and effect relationship if the correlation is
close to 1 or -1.
62.
In order to test the hypothesis that the average body temperature of a healthy
adult is 98.6 degrees, a random sample of 100 healthy adults was selected from
the population of all healthy adults. Suppose that the population standard
deviation for body temperatures is 2 degrees and that the sample mean body
temperature was 98.3.
Find the z statistic that could be used for a one-sample z-test in this situation.
(a) 1.5
63.
(c) 2.001
(d) 2.132
Construct a 90% confidence interval for the population mean, μ. Assume the
population has a normal distribution. In a recent study of 22 eighth graders, the
mean number of hours per week that they played video games was 19.6 with a
standard deviation of 5.8 hours.
(a)
(b)
(c)
(d)
64.
(b) 1.89
(19.62, 23.12)
(17.47, 21.73)
(5.87, 7.98)
(18.63, 20.89)
none are correct:
a z-interval would be (17.566, 21.634)
The probability of making a Type I error is the same as the significance level
(alpha) of a hypothesis test and is the probability of….
(a)
(b)
(c)
(d)
Accepting the alternative hypothesis.
Accepting the null hypothesis when the null hypothesis is true.
Rejecting the null hypothesis if the null hypothesis is true.
Rejecting the null hypothesis when the null hypothesis is false.
65.
Which set of circumstances is most likely to result in a narrow confidence
interval?
(a.)
(b.)
(c.)
(d.)
large sample size and a confidence level of .95.
large sample size and a confidence level of .99.
small sample size and a confidence level of .95.
small sample size and a confidence level of .99.
66.
In a survey of recent high school graduates, 60% said that they miss high school.
This estimate has a margin of error of 5%. This result could equivalently be
reported as which interval?
(a)
50%-60%
(b)
(.6, .05)
(c)
(.5, .7)
(d)
55% to 65%
67.
The “error” described by the margin of error of a confidence interval represents…
(a)
over confidence
(b)
random sampling variability
(c)
sampling bias
(d)
voluntary response bias
68.
Suppose a student takes a 30question multiple choice test
and guesses on every question.
(Each question has four
choices.) The graph to the right
shows the proportion of
correct answers for 200
simulated guessing students.
Based on the simulated results,
what is the approximate
probability that that a student
answers 40% or more of the
questions correctly?
(a.)
(b.)
(c.)
(d.)
.05
.10
.15
.30