Math 200 exam1 Spring 2024 (4)
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Math 200 Exam1 Spring 2024
Good Luck To: __________________________________________ For each of the following circle the letter of the appropriate answer.
1.
In a study of placebos, patients with Parkinson's disease, a movement disorder, were randomly divided into two groups. Each group was given identical placebo saline injections. However, one group was told their injection cost $100 per dose while the other group was told their injection cost $1500 per dose. Patients were then given a motor skills test to determine the effect. What type of study is this?
a.
Observational study
b.
Experiment
2.
Do karaoke singers who are more animated receive more applause from the audience? To answer this, researchers visited a karaoke establishment and rated each karaoke singer with respect to how animated they were. They also used a decibel meter to determine how much applause each singer got. What type of study is this?
a.
Observational study
b.
Experiment
3.
Which of the following is true about samples? a.
The population is a subset of the sample. b.
Data from people in the sample are used to gain information about the population.
c.
Everyone in the population must also be in the sample.
d.
Data from people in the population are used to gain information about the sample.
4.
A census differs from a sample because:
a.
A census can be done any time, but a sample is only done every 10 years.
b.
A census is only done every 10 years, but a sample can be done any time.
c.
In a census the entire population is measured, but in a sample only a portion of the population
is measured.
d.
In a census only a portion of the population is measured, but in a sample the entire population
is measured.
Page 1
Questions 5 and 6 refer to the following situation
A professor asked a sample of 35 college students taking a statistics course how many hours they study outside of the classroom. He also recorded the final grade each student received for the course. The results showed that students who study more tend to get higher course grades.
5.
Which of the following best describes the population for this study?
a.
The statistics students’ course grades.
b.
How much time the students spend studying outside of the classroom.
c.
The 35 statistics students surveyed
d.
All statistics students at this college
6.
Which of the following is not an appropriate conclusion of this study?
a
A lower course grade is linked to lower time spent studying outside of the classroom.
b.
Studying less outside of class causes a student’s course grade to drop.
c.
A higher course grade is associated with student’s studying more outside of classroom.
Questions 7 through 10 refer to the following situation
In a study of animal-assisted therapy for Post Traumatic Stress Disorder, 50 people with PTSD were randomly divided into two groups of 25. One group was given a companion dog to accompany them while the other was not. After a 10-week period all subjects were given a PTSD assessment test by a clinician who was not told whether the subjects had received a companion dog or not.
7.
Suppose subjects are randomly assigned to one of the three groups. This experiment would be
a.
Double blind as long as the subjects are not told the results of the PTSD assessment test.
b.
Single blind because the subjects know whether they received a companion dog or not.
c.
Neither single nor double blind.
d.
Single blind as long as the subjects are not told the results of the PTSD assessment test.
Page 2
8.
Which of the following is not a potential confounding variable?
a.
Whether or not the subject received a companion dog.
b.
The sex of the subjects
c.
The age of the subjects.
d.
The source of the subject’s PTSD.
9.
Which answer best describes why you would want to include a control group?
a.
To decrease the variability of the typical subject’s stress level.
b.
To provide a baseline for comparison of the other two groups.
c.
To eliminate the effect of the treatment.
d.
To control for subject’s bias.
10. Which of the following statements is not true:
a.
Confounding variables were controlled by random assignment to treatments.
b.
The treatment variable is whether or not the subject received a companion dog.
c.
The explanatory variable is the subjects’ sex.
d.
The response variable is the result of the PTSD assessment test.
Page 3
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Questions 1 – 5 refer to the following situation:
The following dotplot represents the number of people in a guided tour of a small museum for a sample of tours.
11. Which of the following describes the shape of the distribution represented by the dot plot?
a.
centered b. skewed to the left
c.
skewed to the right d.
symmetric 12. How many tours are in the sample?
a.
14
b.
15
c.
39
d.
cannot tell
13. What is the range of these data?
a.
14
b.
15
c.
39
d.
cannot tell
14. What is the median of these data?
a.
4
b.
5
c.
6
d.
6.5
15. What is the mean of these data?
a.
4
b.
5
c.
6 d.
6.5
Page 4
Questions 16 – 19 refer to the following situation:
The following boxplots represent the scores on a standardized physical fitness test for the students of
three different schools.
16. Which school has the largest interquartile range for physical fitness scores?
a. School A
b. School B
c. School C
17. Which school has a median physical fitness score of 8? a. School A
b. School B
c. School C
18. Which school would you expect to have the highest standard deviation?
a. School A
b. School B
c. School C
19. What percentage of School A students score lower than the top 75% of the students in School B?
a. 25%
b. 50%
c. 75%
d.
100%
20. The Ironman Triathlons have two divisions, one for professionals and one for amateurs. Which division would most likely have the larger standard deviation in time to finish the triathlon?
a. The professional division would more likely have a higher standard deviation in time to finish. b. The amateur division would more likely have a higher standard deviation in time to finish.
c. The two divisions would likely have the same standard deviation in time to finish.
d. There is not enough information to tell. Page 5
21. A sample of 21 community college students was asked how many days of the week they exercise for at least 20 minutes with the following results.
0
0
0
0
0
0
1
1
2
2
2
2
2
3
3
4
4
4
5
6
7
a.
Using the axis below, draw a dotplot of these data.
a.
Describe the data distribution in terms of center, shape, and spread.
Page 6
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22. The National Institutes of Health gathered data on the favorite lunchtime foods of a group of boys over ten years old, as shown by the bar chart below. Complete the table with the (approximate) frequencies for each category of food, along with their corresponding relative frequencies.
Source:
“Lunch with a Punch”, National Institutes of Health
, http://www.cc.nih.gov/scienceexpo/results.shtml
Food
Frequency
Relative
Frequency
Fish & vegetables
Chicken nuggets
Salad
Pizza
Hot dog
Wrap
Total
Page 7
23. The heights in inches of a sample 17 male students from a liberal arts math class are given in the table below.
73
77
69
79
75
67
71
71
73
73
75
64
69
69
71
74
71
a.
Determine the five-number summary for these data.
Minimum
Q1
Median
Q3
Maximum
b.
Determine the mean, IQR and the Standard Deviation of these data.
Mean
IQR
Standard Deviation
c.
Compute the lower fence, the upper fence, and detect any outliers.
Page 8
24.
There are indications that food allergies are on the rise in the United States. Foods such as nuts, shellfish, wheat, and eggs account for most of the allergies. Allergic reactions to food can range from mild nuisances such as sneezing, to more serious reactions such as difficulty breathing,
and possibly death.
Government agencies and researchers use statistical data to help them better understand the causes of food allergies and to develop better treatments for people that suffer from food allergies.
In a recent survey researchers collected data for 21,875 children under 18 years old. The results show that 831 males have food allergies, and 897 females have food allergies. Use this information to construct a two-way table organized using the following two variables: (1) whether
the child is male or female, and (2) whether the child has a food allergy or does not have a food allergy. It is important to know that 51.3% of the of the children in the survey are males.
Sources: National Center for Health Statistics (NCHS) Data Brief, October 2008, http://www.cdc.gov/nchs/data/databriefs/db10.pdf
National Health Interview Survey, http://www.cdc.gov/nchs/nhis/about_nhis.htm
a. Fill in the data that is known, then calculate and enter the remaining values to complete the table.
Show all work.
Male
Female
TOTAL
no food allergy
food allergy
TOTAL
b.
Based on the table in problem (24) above, what is the probability that a randomly chosen male child under 18 years old will have food allergies?
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