Introduction to Statistics

This evaluation will cover the lessons in this unit. It is open book, meaning you can use your
textbook, syllabus, and other course materials. You will need to understand, analyze, and apply the
information you have learned in order to answer the questions correctly. To submit the evaluation by
mail, follow the directions on your Enrollment Information Sheet. To take the evaluation online,
access the online version of your course; use the navigation panel to access the prep page for this
evaluation and follow the directions provided.
Multiple-Choice
Select the response that best completes the statement or answers the question.
_ 1. On July 7, 2010, The Gallup organization conducted a telephone poll of 1,007 random adults in all 50 U.S. states and the District of Columbia. They found that 38% strongly opposed the federal government suing Arizona over their new immigration law. Which is true? I. The population of interest is all U.S. adults. II. 38% is a statistic and not the actual percentage of all U.S. adults who strongly oppose the lawsuit. III. This sampling design should provide a reasonably accurate estimate of the actual percentage of all U.S. adults who strongly oppose this lawsuit. a. I, II, and III b. I and II c. I only d. II only 2. A school district has three high schools. The district decides to randomly test high school
students for attention deficit disorder (ADD). The school board creates a list of all of the
students from the three high schools and randomly samples 250 students from that list.
Is this a simple random sample?
a. Yes, because students were chosen at random.
b. No, because we can’t guarantee that there are students from each school in the
sample.
c. Yes, because this method could choose any 250 high school students from
throughout the district.
d. No, because we can’t guarantee that there are students from each high school
grade in the sample.
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3. A chemistry professor who teaches a large lecture class gives a survey during class about
how he can make the class more interesting. He is hoping he can get more students to
attend his class. This survey method suffers from which of the following?
a. voluntary response bias
b. nonresponse bias
c. response bias
d. undercoverage
Use this information to answer questions 4-7.
A statistics teacher wants to know how her students feel about an introductory statistics
course. She decides to administer a survey to a random sample of students taking the
course. She has several sampling plans to choose from. Name the sampling strategy in
each.
4. There are four grade levels of students taking the class: freshmen, sophomores, juniors,
and seniors. Randomly select 15 students from each grade level.
a. cluster sampling
b. simple random sampling
c. systematic sampling
d. stratified sampling
5. Randomly select a grade level (freshmen, sophomores, juniors, and seniors) and survey
every student in that grade level.
a. cluster sampling
b. simple random sampling
c. systematic sampling
d. stratified sampling
6. Each student has a nine-digit student number. Randomly choose 60 numbers.
a. cluster sampling
b. simple random sampling
c. systematic sampling
d. stratified sampling
7. Using the class roster, select every fifth student from the list.
a. cluster sampling
b. simple random sampling
c. systematic sampling
d. stratified sampling
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8. Suppose the state decides to randomly test high school wrestlers for steroid use. There
are 16 teams in the league, and each team has 20 wrestlers. State investigators plan
to test 32 of these athletes by randomly choosing two wrestlers from each team. Is this
a simple random sample?
a. Yes, because the wrestlers were chosen at random.
b. Yes, because each wrestler is equally likely to be chosen.
c. No, because not all possible groups of 32 wrestlers could have been the sample.
d. No, because a random sample of teams was not first chosen.
9. Which statement about bias is true?
I. Bias results from random variation and will always be present.
II. Bias results from a sampling method likely to produce samples that do not
represent the population.
III. Bias is usually reduced when the sample size is larger.
a. I and III
b. II and III
c. I only
d. II only
10. The owner of a car dealership planned to develop strategies to increase sales. He hoped
to learn the reasons why many people who visit his car lot do not eventually buy a car
from him. For one month he asked his sales staff to keep a list of the names and
addresses of everyone who came in to test drive a car. At the end of the month he sent
surveys to the people who did not buy a car, asking them why. About one third of them
returned the survey, with 44% of those indicating that they found a lower price
elsewhere. Which is true?
I. The population of interest is all potential car buyers.
II. This survey design suffered from non-response bias.
III. Because it comes from a sample 44% is a parameter, not a statistic.
a. I and II
b. II and III
c. I, II, and III
d. none of the above
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Use this information to answer questions 11-14.
Management at a retail store is concerned about the possibility of drug abuse by people who work
there. They decide to check on the extent of the problem by having a random sample of the
employees undergo a drug test. Several plans for choosing the sample are proposed. Name the
sampling strategy in each.
11. Randomly select an employee classification and test all the people who work in that
classification – supervisors, full-time clerks, part-time clerks, and maintenance staff.
a. cluster sampling
b. systematic sampling
c. stratified sampling
d. simple random sampling
12. Choose the fourth person that arrives to work for each shift.
a. cluster sampling
b. systematic sampling
c. stratified sampling
d. simple random sampling
13. There are four employee classifications: supervisors, full-time clerks, part-time clerks,
and maintenance staff. Randomly select ten people from each category.
a. cluster sampling
b. systematic sampling
c. stratified sampling
d. simple random sampling
14. Each employee has a three-digit identification number. Randomly choose 40 numbers.
a. cluster sampling
b. systematic sampling
c. stratified sampling
d. simple random sampling
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Use this information to answer questions 15 – 19.
Researchers who wanted to see if drinking grape juice could help people lower their blood pressure
got 120 non-smokers to volunteer for a study. They measured each person’s blood pressure and
then randomly divided the subjects into two groups. One group drank a glass of grape juice every
day while the other did not. After sixty days the researchers measured everyone’s blood pressure
again. They reported that differences in changes in blood pressure between the groups were not
statistically significant.
15. Was this an experiment or an observational study? Explain.
a. observational; observed 120 non-smokers
b. observational; volunteers caused this study to be biased
c. experimental; treatments were applied
d. experimental; one group/all non-smokers
16. What is meant by “not statistically significant” in this context?
a. The differences were large since this lasted 60 days.
b. There were not many subjects involved.
c. Only non-smokers were included so this could not be expanded to the general
population.
d. The results were small enough that they could easily be attributed to variability, not
the grape juice.
17. Why did the researchers randomly assign the subjects to the groups?
a. This equalizes the effects of variables for which were not controlled.
b. This was easier.
c. They could keep track of who was in which group easier.
d. Not everyone liked grape juice.
18. Why did they have a group that was not drinking grape juice?
a. They did not like grape juice.
b. They needed a control group to compare with the treatment group.
c. This was a placebo since they all needed something.
d. In order for the experiment to be valid, it needed to be confounded.
19. Why did the researchers study only non-smokers?
a. They wanted to limit the number of subjects in the experiments.
b. That would result in variability.
c. The smokers were used as a control.
d. Smoking tends to affect blood pressure. It might have confounded the results.
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20. In an experiment the primary purpose of blocking is to reduce ___
.
a. bias
b. randomness
c. variation
d. undercoverage
_ 21. 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 diets for several years to see if any developed thyroid problems. This is a(n) ____.
a. prospective study
b. retrospective study
c. randomized experiment
d. survey
_ 22. Which of the following is not required in an experimental design? a. control b. replication c. randomization d. blocking 23. A headline in a local newspaper announced “Video game playing can lead to better
spatial reasoning abilities.” The article reported that a study found “statistically
significant differences” between teens who play video games and teens who do not,
with teens who play video games testing better in spatial reasoning. Do you think the
headline was appropriate? Explain.
a. No, there was no control group.
b. No, this is an observational study which cannot imply causation.
c. Yes, there was a statistically significant difference.
d. Yes, there were two groups, one of which was a control group.
24. In an experiment, a placebo is used to ____
.
a. speed the rate of the experiment
b. eliminate confounding
c. assist in blinding
d. increase blocking
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_ 25. A researcher wants to compare the performance of three types of pain relievers in
volunteers suffering from arthritis. Because people of different ages may suffer arthritis
of varying degrees of severity, the subjects are split into two groups: under 60 and over

  1. Subjects in each group are randomly assigned to take one of the medications.
    Twenty minutes later they rate their levels of pain. This experiment _.
    a. is completely randomized
    b. has one factor (medication) blocked by age
    c. has two factors, medication and age
    d. has one factor (age) blocked by medication type
    _ 26. Can watching a movie temporarily raise your pulse rate? Researchers have 50 volunteers check their pulse rates. Then they watch an action film, after which they take check their pulse rates once more. Which aspect of experimentation is present in this research? a. a placebo b. blinding c. randomization d. none of these Use the following information to answer questions 27 – 30. A study was created to test the effects of jazz on people’s sleep patterns. The hypothesis of the experiment was that if people listened to jazz music as they fall asleep, they will sleep for longer periods of time. For the experiment, 2 groups of people were created. One group was placed in a quiet room where they went to sleep and they were timed on how long they slept. The other group was placed in a room where jazz music played softly as they began to sleep and played throughout the night. As each group awoke, their sleep times were monitored.
    27. What is the factor in this case?
    a. sleep patterns
    b. sleep times
    c. jazz played
    d. 2 groups of people
    28. What is the response variable?
    a. jazz played
    b. sleep times
    c. 2 groups of people
    d. quiet room
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    29. What is the control group?
    a. The group with no jazz while sleeping.
    b. The group listening to jazz.
    c. The group that was given placebos.
    d. The group that was blinded.
    30. What is the experimental group?
    a. The group in the experiment.
    b. The group in the quiet room.
    c. The group that was given placebos.
    d. The group who listened to jazz while sleeping.
    31. What control was used in this experiment?
    Shortly after Ms. Berndt’s cat, Revere, was born, Ms. Berndt realized Revere wasn’t
    eating enough. She went to the pet store and bought many different kinds of food and
    fed Revere different types every day. Each day she noted the type of food and how
    much Revere ate out of his dish. Eventually Revere ate a lot of the CreppyCat brand
    food and Ms. Berndt bought that for him from then on. Revere is the best worst cat
    ever.
    a. Revere was not eating cat food.
    b. CreppyCat brand food.
    c. Many different kinds of food.
    d. There is no control group.
    32. It’s a common belief that people behave strangely when there’s a full moon and that as a
    result police and emergency rooms are busier than usual. If you wanted to find out
    whether there is any value to this belief, what kind of study would you use and why?
    a. experiment; use as a control, those days when there is no full moon
    b. experiment; use blinding and don’t tell anyone what you are looking for
    c. prospective observational study; find out which days are full moon days and talk
    with officers and emergency room personnel
    d. retrospective observational study; it is easier to go back three years to find data to
    support this belief
    33. A swimsuit manufacturer wants to test the speed of its newly designed swimsuit. The
    company designs an experiment by having 6 randomly selected Olympic swimmers
    swim as fast as they can in their old suits first, and then swim the event again with the
    new, expensive swimsuit. The company will use the difference in times as the
    response variable. Which of the following is present in this experiment?
    a. blinding
    b. an explanatory variable
    c. blocking
    d. a placebo
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    34. Before drilling for water, many rural homeowners hire a dowser (a person who claims to
    sense the presence of underground water using a forked stick). Suppose we wish to
    set up an experiment to test one dowser’s ability. We get 20 identical containers, fill
    some with water, and ask him to identify which containers have water. The dowser
    correctly identifies the contents of 11 out of 20 containers. Is this level of success
    statistically significant? Explain.
    a. no, he needs to replicate the experiment
    b. no, 55% (11/20) is not much better than 50% (10/20)
    c. yes, that is better than the mean
    d. yes, anything above 0% is great
    35. Which of the following studies is experimental?
    a. Incidences of cancer in people who lived near a chemical factory are compared to
    those who did not live near this factory.
    b. The weights of school athletes and non-athletes are compared.
    c. A survey examines if doctors with different specialties have different stress levels.
    d. Similar patients with high blood pressure are randomly given three different doses of
    a new drug and their blood pressure is observed.
    36. In an experiment the primary purpose of blinding is to reduce ___
    .
    a. randomness
    b. variation
    c. bias
    d. confounding
    _ 37. In an experiment the primary purpose of blocking is to reduce ____.
    a. bias
    b. randomness
    c. factors
    d. variation
    _ 38. In an experiment, the best way to reduce confounding is to use ____.
    a. a placebo
    b. a control group
    c. randomization
    d. a response variable
    _ 39. You want to compare the average ages of the math and science teachers at your local high school. Which is the best method to collect the data? a. sample survey b. census c. simulation d. observational study Unit 3 Evaluation 246 MTHH 041 40. Among a dozen eggs, three are rotten. A recipe calls for two eggs; they’ll be selected
    randomly from the dozen. Which plan could be used to simulate the number of rotten
    eggs that might be chosen?
    I. Let 0, 1, and 2 represent the rotten eggs; 3, 4, 5, 6, 7, 8, 9, 10, and 11 represent the
    good eggs. Generate two random numbers 0-11, ignoring repeats.
    II. Randomly generate a 0, 1, or 2 to represent the number of rotten eggs you get.
    III. Since 25% of the eggs are rotten, let 0 = rotten and 1, 2, 3 = good. Generate two
    random numbers 0-3 and see how many 0’s you get.
    a. III
    b. II
    c. I
    d. I and III only
    41. Hannah wants to simulate whether customers will choose a small, medium, or large
    drink, or no drink at a fast food restaurant. She decides to use digits from a random
    number table to represent the drink option a customer will order (0=no drink, 1=small
    drink, 2=medium drink, 3=large drink, ignore digits 4-9) Why does this NOT model the
    situation?
    a. The choices are not equally likely to occur.
    b. Some of the digits were ignored.
    c. The choice are independent of each other.
    d. Some customers had more than one drink.
    42. Does donating blood lower cholesterol levels? 50 volunteers have a cholesterol test,
    then donate blood, and then have another cholesterol test. Which aspect of
    experimental design is present?
    a. blocking
    b. randomization
    c. blinding
    d. none of these
    43. In a simulation of a couple who is willing to have as many children as necessary to have
    two girls, how could you assign digits to estimate the average number of children
    required to have two girls?
    a. Assign the even digits 0, 2, 4, 6, 8 to boys and the odd digits 1, 3, 5, 7, 9 to girls.
    b. Assign digits 0-5 to girls and 6-9 to boys.
    c. Assign digits 00-50 to girls and 51-99 to boys.
    d. Assign digits 1-50 to girls and 51-99 to boys.
    Unit 3 Evaluation 247 MTHH 041
    Use this information to answer questions 44 – 46.
    The Mars candy company starts a marketing campaign that puts a plastic game piece in each
    bag of M&Ms. 25% of the pieces show the letter “M”, 10% show the symbol “&”, and the rest
    just say “Try again”. When you collect a set of three symbols “M”, “&”, and “M” you can turn
    then in for a free bag of candy. Below is the information obtained from the simulation for the 2
    trials.
    Trial # The run
    1 69074 91976 33584 94138 87637
    2 48324 77938 31249 64710 02295
    44. How could you assign random numbers to estimate the average number of bags a
    consumer would have to buy to get a free one?
    a. Assign 0-9 to pieces with “M”, 10-13 to pieces with “&”, and 14-39 to pieces with
    “Try again”.
    b. Assign 00-24 to pieces with “M”, 25-34 to pieces with “&”, and 35-99 to pieces with
    “Try again”.
    c. Assign 00-24 to pieces with “M” and 25-99 to all other pieces.
    d. none of these
    45. Assume that you chose the correct assignment of random numbers in Q44, what are
    your outcomes for Trial 1 and Trial 2?
    a. Trial 1 outcome = 6, and Trial 2 outcome = 7
    b. Trial 1 outcome = 9, and Trial 2 outcome = 7
    c. Trial 1 outcome = 7, and Trial 2 outcome = 6
    d. Trial 1 outcome = 6, and Trial 2 outcome = 10
    46. About how many bags will a consumer have to buy to get a free one?
    a. average 7.5 bags
    b. average 6.5 bags
    c. average 8 bags
    d. average 7 bags
    47. Your state’s BigBucks Lottery prize has reached $100,000,000, and you decide to play.
    You have to pick five numbers between 1 and 60, and you’ll win if your numbers match
    those drawn by the state. You decide to pick your “lucky” numbers using a random
    number table. Which numbers do you play, based on these random digits?
    43680 98750 13092 76561 58712
    a. 43, 9, 50, 13, 27
    b. 43, 68, 9, 87, 50
    c. 4, 3, 6, 8, 0
    d. 43, 98, 13, 76, 58
    Unit 3 Evaluation 248 MTHH 041
    Use this information to answer questions 48 – 50.
    You take a quiz with 6 multiple choice questions. After you studied, you estimated that you
    would have about an 80% chance of getting any individual question right. Below is the
    information obtained from the simulation for the 7 trials.
    Trial # The run
    1 07196 98642
    2 23185 56282
    3 14125 38872
    4 71622 35940
    5 72753 32616
    6 89059 43528
    7 39717 37348
    48. How would you use the random digits to represent the 80% chance that you get the
    answer right?
    a. none of these
    b. Assign random digits 0-10. Let 0-7 = right and 8-10 = wrong.
    c. Assign random digits 0-9. Let 0-6 = right and 7-9 = wrong.
    d. Assign random digits 0-9. Let 0-7 = right and 8-9 = wrong.
    49. Assume that you chose the correct assignment of random digits in Q48, out of the 7
    trials, how many trial outcomes did you get all 6 questions right?
    a. 1
    b. 4
    c. 3
    d. 0
    _
    50. What are your chances of getting all 6 right? Based on the outcomes of the 7 trials.
    a. about 57%
    b. about 43%
    c. about 75%
    d. about 25%
    Carefully check your answers on this evaluation and make any corrections you feel are
    necessary. When you are satisfied that you have answered the questions to the best of your
    ability, transfer your answers to an answer sheet. Please refer to the information sheet that
    came with your course materials.
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