MCJ5100 Advance Research Methods and Analysis I
Final Exam Review: Winter Quarter 2020
Identify the population and sample in the following study.
1. A study of dietary habits of 20,000 men was conducted to find link between high
intakes of dairy products and prostate cancer.
Determine whether the numerical value is a parameter or a statistic.
2. In a survey of 2253 Internet users, 19% use Twitter or another service to share
social updates.
3. At college 90% of the Board of Trustees members approved the contract of the
new president.
Determine whether the data are qualitative or quantitative.
4. A list of debit card pin numbers.
5. The final scores on a video game.
Identify each data’s level of measurement (nominal, ordinal, interval, ratio)
6. A list of badge numbers of police officers at a precinct.
7. The horespowers of racing car engines.
8. The top 10 grossing films released in 2019.
1
9. The years of birth for the numbers in the Boston marathon.
Determine which method of data collection (observation, experiment, stimulation, survey)
you would use to gather data for each study.
10. A study on the effect of low dietary intake of vitamin C and iron on lead levels in
adults.
11. The ages of people living within 500 miles of your home.
Identify the sampling technique used in each study.
12. A journalist goes to a campground to ask people how they feel about air pollution.
13. For quality assurance, every tenth machine part is selected from an assembly line
and measured for accuracy.
14. A study of attitudes about smoking is conducted at a college. The students are
divided by class (freshman, sophomore, junior, and senior). Then a random sample is
selected from each class and interviewed.
15. The data set represents the number of minutes a sample of 25 people exercise
each week.
108
157
127
139
150
128
120
124
139
123
111
119
120
101
118
132
135
114
123
119
127
131
116
131
117
a. Make a frequency distribution of the data set using five classes. Include
class limits, midpoints, boundaries, frequencies, relative frequencies,
cumulative frequency, and class boundaries.
2
Class
Frequency
(f)
Midpoint
Relative
Frequency
Cumulative
Frequency
Class
Boundaries
b. Display the data using a frequency histogram.
c. Describe the distribution’s shape as symmetric, uniform, or skewed.
d. Display the data using a stem-and-leaf plot. Use the first two numbers of
each number (For example 115, use “11”)
e. Use the frequency distribution formulas to find the sample mean and the
sample standard deviation of the data set.
3
16. Weekly salaries salaries (in dollars) for a sample of registered nurses are listed.
774 446 1019 795 908 667 444 960
a. Find the mean, median, mode of the salaries.
i.
Mean =
ii.
Median =
iii.
Mode =
b. Find the range, variance, and standard deviation of the data set.
i.
Range =
ii.
Variance =
iii.
Standard Deviation =
c. Interpret the results in the context of the real-life setting.
17. The mean price of new homes from a sample of houses is $155,000 with a standard
deviation of $15,000. The data set has a bell-shaped distribution. Use the
z-scores to determine which, if any, of the following house prices is unusual.
a. $200,000
i.
Z=
b. $55,000
i.
Z=
18. The number of regular season wins for each Major League Baseball team in 2009
are listed.
a. Find the five-number summary of the data set.
i.
Min =
ii.
Q1 =
iii.
Q2 =
iv.
Q3 =
v.
Max =
b. Find the interquartile range.
i.
c. Display the data using a box-and-whisker-plot.
19. Identify the sample space of the probability experiment and determine the number
of outcomes in the event. Draw a tree diagram if it is appropriate.
4
a. Experiment: Tossing four coins.
b. Event: Getting three heads.
i.
Sample space:
20. Use the fundamental counting principle: A student must choose from 7 classes to
take at 8:00 a.m., 4 classes to take at 9:00 a.m., and 3 classes to take at 10:00 a.m.
How many ways can the student arrange the schedule?
21. Classify the statement as an example of classical probability, empirical probability,
or subjective probability.
a. On the basis of prior counts, a quality control says there is a 0.05
probability that a randomly chosen part is defective.
b. The probability of randomly selecting five cards of the same suit from a
standard deck is about 0.0005.
c. The chance that Corporation A’s stock price will fall today is 75%.
5
22. The table below shows the number (in thousands) of earned degrees, by level and
gender, conferred in the United States in a recent year.
Level of Degree
Gender
Male
Gender
Female
Total
Associate’s
275
453
728
Bachelor’s
650
875
1525
Master’s
238
366
604
Doctoral
30
30
60
Total
1193
1724
2917
A person who earned a degree in the year is randomly selected. Find the
probability of selecting someone who:
a. Earned a bachelor’s degree given that the person is a female.
b. Earned an associate’s degree or a bachelor’s degree.
c. Earned a doctorate given that the person is a male.
23. Decide if the events are mutually exclusive. Then decide if the events are
independent or dependent.
a. Event A: A golfer scoring the best round in a four-round tournament.
b. Event B: Losing the golf tournament.
24. The access code for a warehouse’s security system consists of six digits. The first
digit cannot be 0 and the last digit must be even. How many different codes are
available?
25. From a pool of 30 candidates, the offices of president, vice president, secretary,
and treasurer will be filled. In how many ways can the offices be filled?
6
26. 11P2
27. 5C3/10C3
28. A card is randomly selected from a standard deck. Find the probability that the
card is red or a queen.
29. A 12-sided die, number 1 to 12, is rolled. Find the probability that the roll results
in an odd number of a number less than 4.
30. Five players on a basketball must each choose a player on the opposing team to
defend. In many ways can they choose their defensive assignments?
31. Decide whether the random variable x is discrete or continuous.
a. Let x represent the amount of carbon dioxide emitted from a car’s tailpipe
each day.
b. Let x represent the number of people that activate a metal detector at an
airport each hour.
32. Decide whether the distribution is a probability distribution. If it is not, identify
the property that is not satisfied.
x
1
2
3
4
5
6
7
8
P(x)
1/80
2/75
1/10
12/25
27/30
1/5
2/25
1/120
7
33. Determine the probability distribution that is missing.
x
0
1
2
3
4
P(x)
0.07
0.20
.38
?
0.13
34. The number of televisions per household in a small town.
Television
0
1
2
3
Households
26
442
728
1404
Use the probability distribution or histogram to find the:
a.
b.
c.
d.
Mean
Variance
Standard deviation
Expected value
35. To left of z = 0.33
36. To The right of z = 3.22
37. Between z = -1.55 and z = 1.04
38. Determine whether the hypothesis test with the given null and alternative
hypothesis is left-tailed, right tailed, or two tailed.
a. Ho:p=0.25
Ha:p≠0.25
39. Determine whether the hypothesis test with the given null and alternative
hypothesis is left-tailed, right tailed, or two tailed.
a. Ho:μ≤8.0
Ha:μ>8.0
40. Write the claim as a mathematical sentence.
a. A light bulb manufacturer claims that the mean life of a certain light bulb is
more than 750 hours.
8
b. A stated by a company’s shipping department, the number of shipping errors
per million shipments has a standard deviation that is less than 3.
c. The standard deviation of the base price of a certain type of all-terrain
vehicle is no more than $320.
9
MCJ5100 Advance Research Methods and Analysis I
Final Exam Review: Winter Quarter 2020
Identify the population and sample in the following study.
1. A study of dietary habits of 20,000 men was conducted to find link between high
intakes of dairy products and prostate cancer.
Determine whether the numerical value is a parameter or a statistic.
2. In a survey of 2253 Internet users, 19% use Twitter or another service to share
social updates.
3. At college 90% of the Board of Trustees members approved the contract of the
new president.
Determine whether the data are qualitative or quantitative.
4. A list of debit card pin numbers.
5. The final scores on a video game.
Identify each data’s level of measurement (nominal, ordinal, interval, ratio)
6. A list of badge numbers of police officers at a precinct.
7. The horespowers of racing car engines.
8. The top 10 grossing films released in 2019.
1
9. The years of birth for the numbers in the Boston marathon.
Determine which method of data collection (observation, experiment, stimulation, survey)
you would use to gather data for each study.
10. A study on the effect of low dietary intake of vitamin C and iron on lead levels in
adults.
11. The ages of people living within 500 miles of your home.
Identify the sampling technique used in each study.
12. A journalist goes to a campground to ask people how they feel about air pollution.
13. For quality assurance, every tenth machine part is selected from an assembly line
and measured for accuracy.
14. A study of attitudes about smoking is conducted at a college. The students are
divided by class (freshman, sophomore, junior, and senior). Then a random sample is
selected from each class and interviewed.
15. The data set represents the number of minutes a sample of 25 people exercise
each week.
108
157
127
139
150
128
120
124
139
123
111
119
120
101
118
132
135
114
123
119
127
131
116
131
117
a. Make a frequency distribution of the data set using five classes. Include
class limits, midpoints, boundaries, frequencies, relative frequencies,
cumulative frequency, and class boundaries.
2
Class
Frequency
(f)
Midpoint
Relative
Frequency
Cumulative
Frequency
Class
Boundaries
b. Display the data using a frequency histogram.
c. Describe the distribution’s shape as symmetric, uniform, or skewed.
d. Display the data using a stem-and-leaf plot. Use the first two numbers of
each number (For example 115, use “11”)
e. Use the frequency distribution formulas to find the sample mean and the
sample standard deviation of the data set.
3
16. Weekly salaries salaries (in dollars) for a sample of registered nurses are listed.
774 446 1019 795 908 667 444 960
a. Find the mean, median, mode of the salaries.
i.
Mean =
ii.
Median =
iii.
Mode =
b. Find the range, variance, and standard deviation of the data set.
i.
Range =
ii.
Variance =
iii.
Standard Deviation =
c. Interpret the results in the context of the real-life setting.
17. The mean price of new homes from a sample of houses is $155,000 with a standard
deviation of $15,000. The data set has a bell-shaped distribution. Use the
z-scores to determine which, if any, of the following house prices is unusual.
a. $200,000
i.
Z=
b. $55,000
i.
Z=
18. The number of regular season wins for each Major League Baseball team in 2009
are listed.
a. Find the five-number summary of the data set.
i.
Min =
ii.
Q1 =
iii.
Q2 =
iv.
Q3 =
v.
Max =
b. Find the interquartile range.
i.
c. Display the data using a box-and-whisker-plot.
19. Identify the sample space of the probability experiment and determine the number
of outcomes in the event. Draw a tree diagram if it is appropriate.
4
a. Experiment: Tossing four coins.
b. Event: Getting three heads.
i.
Sample space:
20. Use the fundamental counting principle: A student must choose from 7 classes to
take at 8:00 a.m., 4 classes to take at 9:00 a.m., and 3 classes to take at 10:00 a.m.
How many ways can the student arrange the schedule?
21. Classify the statement as an example of classical probability, empirical probability,
or subjective probability.
a. On the basis of prior counts, a quality control says there is a 0.05
probability that a randomly chosen part is defective.
b. The probability of randomly selecting five cards of the same suit from a
standard deck is about 0.0005.
c. The chance that Corporation A’s stock price will fall today is 75%.
5
22. The table below shows the number (in thousands) of earned degrees, by level and
gender, conferred in the United States in a recent year.
Level of Degree
Gender
Male
Gender
Female
Total
Associate’s
275
453
728
Bachelor’s
650
875
1525
Master’s
238
366
604
Doctoral
30
30
60
Total
1193
1724
2917
A person who earned a degree in the year is randomly selected. Find the
probability of selecting someone who:
a. Earned a bachelor’s degree given that the person is a female.
b. Earned an associate’s degree or a bachelor’s degree.
c. Earned a doctorate given that the person is a male.
23. Decide if the events are mutually exclusive. Then decide if the events are
independent or dependent.
a. Event A: A golfer scoring the best round in a four-round tournament.
b. Event B: Losing the golf tournament.
24. The access code for a warehouse’s security system consists of six digits. The first
digit cannot be 0 and the last digit must be even. How many different codes are
available?
25. From a pool of 30 candidates, the offices of president, vice president, secretary,
and treasurer will be filled. In how many ways can the offices be filled?
6
26. 11P2
27. 5C3/10C3
28. A card is randomly selected from a standard deck. Find the probability that the
card is red or a queen.
29. A 12-sided die, number 1 to 12, is rolled. Find the probability that the roll results
in an odd number of a number less than 4.
30. Five players on a basketball must each choose a player on the opposing team to
defend. In many ways can they choose their defensive assignments?
31. Decide whether the random variable x is discrete or continuous.
a. Let x represent the amount of carbon dioxide emitted from a car’s tailpipe
each day.
b. Let x represent the number of people that activate a metal detector at an
airport each hour.
32. Decide whether the distribution is a probability distribution. If it is not, identify
the property that is not satisfied.
x
1
2
3
4
5
6
7
8
P(x)
1/80
2/75
1/10
12/25
27/30
1/5
2/25
1/120
7
33. Determine the probability distribution that is missing.
x
0
1
2
3
4
P(x)
0.07
0.20
.38
?
0.13
34. The number of televisions per household in a small town.
Television
0
1
2
3
Households
26
442
728
1404
Use the probability distribution or histogram to find the:
a.
b.
c.
d.
Mean
Variance
Standard deviation
Expected value
35. To left of z = 0.33
36. To The right of z = 3.22
37. Between z = -1.55 and z = 1.04
38. Determine whether the hypothesis test with the given null and alternative
hypothesis is left-tailed, right tailed, or two tailed.
a. Ho:p=0.25
Ha:p≠0.25
39. Determine whether the hypothesis test with the given null and alternative
hypothesis is left-tailed, right tailed, or two tailed.
a. Ho:μ≤8.0
Ha:μ>8.0
40. Write the claim as a mathematical sentence.
a. A light bulb manufacturer claims that the mean life of a certain light bulb is
more than 750 hours.
8
b. A stated by a company’s shipping department, the number of shipping errors
per million shipments has a standard deviation that is less than 3.
c. The standard deviation of the base price of a certain type of all-terrain
vehicle is no more than $320.
9
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