# SOLUTION: KINE 303 UMUC It Important to Learn About Research Methods and Statistics Questions

KINE 303, Fall 2021
Name: ________________________
KINE 303: Statistics and Research Methods
Exam 1
This is a hard deadline and late exams are not accepted without prior approval. The exam should take you about
1.5-2 hours to complete if you previously studied so please plan accordingly to start the exam. There is no time
limit once you start the exam so long as you submit it by the due date/time.
The exam is worth 100 points total, and each question indicates its point value. Read each question carefully and
think about how it relates to topics discussed in lecture. Make sure you answer the question being asked.
completed exam or scan it in to a computer. You must submit the exam as one file on cougar courses.
A few reminders for full credit:

Give the formula you used for each problem that requires the use of a formula
Show ALL of your work – even if you’re using a calculator!
All questions relating to the standard normal distribution must have a normal curve drawn and shaded to
indicate the area you are looking for..
Report final answers to two decimal places (i.e., 1.92) if the answer is not a whole number
THIS IS AN INDIVIDUAL EXAM!!
You should not discuss the exam with classmates or compare answers. If you have questions about anything on
the exam please let me know. I want you all to do well but it is not worth working with others to do well. If you
Initials: ______
1. [5 points] Why is it important to learn about research methods and statistics?
2. [10 points] This is a hypothetical situation. You are interested in learning more about recovery after a
shoulder injury from playing sports. You want to conduct research to better understand what influences
recovery times. Research in this area is limited but other has conducted research on shoulder injuries in
the past.
a. One of the first steps in the scientific method is to conduct background research on what other
research has been conducted. Why is it important to do background research on your topic?
b. If not a lot of research has been done on the topic, would you first conduct an observational
research study or an experimental research study? Why?
c. Briefly compare and contrast the main types of observational studies.
Page 2
Initials: ______
3. [3 points] Is each variable nominal, ordinal, or interval/ratio? Circle/highlight one answer for each.
a. Pain Scale:
Nominal
Ordinal
Interval/Ratio
b. Distance:
Nominal
Ordinal
Interval/Ratio
c. Sex:
Nominal
Ordinal
Interval/Ratio
4. [3 points] Is each variable continuous or discrete? Circle/highlight one answer for each.
a. Number of athletes:
Discrete
Continuous
b. Weight of a box:
Discrete
Continuous
c. Visits to the Emergency Room:
Discrete
Continuous
5. [2 points] Researchers are using an apple watch to understand how a new intervention impact physical
activity and resting heart rate. Which of the following would be a way to assess reliability of the heart
a. Measure heart rate from the same person 10 times having people exercise at different intensities every
time you measure heart rate
b. Measure heart rate from the same person 10 times having people exercise at the same intensity every
time you measure heart rate
c. Compare heart from the apple watch to the results from another smart watch
d. Compare heart from the apple watch to the heat rate obtained from an EKG (Gold standard
measurement)
e. You can’t assess reliability of a new device
6. [2 points] If the probability of event A is P(A)= 0.35 and the probability of a second event B is P(B) =
0.2, what is the probability of event A happening and then event B happening right after?
Page 3
Initials: ______
7. [10 points] You want to assess the validity and reliability of a new measurement tool to measure body fat
a. When collecting data for a research study, why is it important that the measurement tools we use
are both valid and reliable?
b. How would you assess the validity of the new measurement tool to measure body fat %?
c. What type of bias might occur during the process of collecting data from participants?
d.
How can we minimize the type of bias you identified in the question above (c)?
8. [10 points] Two researchers studying diabetes independently draw a convenience sample of 50 adults
over the age of 40, from a large urban area, and determine if they have diabetes. One researcher finds that
4 percent of the adults in their sample have diabetes, and the other finds that 6 percent of adults in their
sample have diabetes. Answer the following questions.
a. What might explain the difference in the percent of adults who have diabetes between the two
samples?
b. What type of bias might affect the results of the study based on how the researchers sampled
participants?
c. Explain the difference between the two major methods of sampling? Should the researchers use a
different method of sampling than they did? Why or why not?
d. What could the researchers do to minimize bias in their sampling process?
Page 4
Initials: ______
9. [15 points total] The data below represent individual 100m run times in seconds:
14.1
12
9.8
11.5
11.3
11.4
10.8
15.6
a. What is the mean [2 points]?
b. What is the median [2 points]?
c. What is the range [2 points]?
d. What is the interquartile range [4 points]?
e. What is the standard deviation [5 points]?
Page 5
Initials: ______
10. [10 points]. Vertical jump height was measured for 500 college students; the mean was 15.8 with a
standard deviation of 4.4 inches.
a. Draw and label the distribution with its mean and standard deviation.
b. How many students jumped less than 14.7 inches? Shade the distribution that you drew in (a) to
indicate what you are looking for. Show all work.
c. What percentile is a vertical jump of 17.8 inches?
11. [7 points] What is the difference between descriptive and inferential statistics? Why do we need to
understand probability to move from descriptive statistics to inferential statistics?
Page 6
Initials: ______
12. [8 points] A group of students attempted to kick 15 field goals. The data representing each student’s
number of successful field goals is listed below. Show work when applicable.
a. What is the mode for the field goal data [2 points]?
b. What is the percentile of a participant who kicked 8 field goals [3 points]?
x
13
8
7
10
10
8
15
c. What number of field goals most closely represents the 34th percentile [3 points]?
6
10
4
3
0
1
3
Page 7
Initials: ______
13. [15 points total] You test 97 people for the number of push-ups they can perform in 60 seconds. You
calculate the mean of your sample to be 32 push-ups with a standard deviation of 9 push-ups.
a. Calculate a 95% confidence interval of the predicted push-ups in the population [5 points]
b. If you wanted to compute the 60% confidence interval of population mean, what value would you
use for Z in your equation [5 points]? Calculate the 60% confidence interval.
c. Which confidence interval is narrower, the 60% or the 95% confidence interval? Why? [2 points]
d. Why do we calculate confidence intervals? [3 points]
Page 8
KINE 303
Question 1: Calculate the mean, median, mode, range, and interquartile range of the data on age
from a population below. What do the mean and median tell you about the distribution of the
data? (Will it be skewed?) Calculate the standard deviation, and a 95% confidence interval.
33
18
19
40
29
44
21
29
29
33
28
32
24
36
100
Step 1: Rank Order Data: 18, 19, 21, 24, 28, 29, 29, 29, 32, 33, 33, 36, 40, 44, 100
n=15
𝟓𝟏𝟓
̅) =
Mean (𝑿
= 34.33 years
𝟏𝟓
Median=(29+29)/2= 29 years
The distribution will be slightly right skewed as the mean is larger than the median. This is
happening because there is a potential outlier in the data, which is a person who is 100
years old.
Mode=29 years
Min=18 years
Max=100 years
Range=100-18=82 years
IQR=36-24=12 years
-Two ways to calculate IQR
Method 1:
1) First calculate position on the rank order distribution for the 25th and 75th
percentile: n+1/4=16/4=4
2) 18, 19, 21, 24, 28, 29, 29, 29, 32, 33, 33, 36, 40, 44, 100
-Count to the fourth position from the top and bottom of the distribution.
Method 2:
-Calculate the third quartile 3rd quartile as 75%tile=.75*15=11.25 (round up to12th
space)
-Calculate the 1st quartile as 25%tile=.25*15=3.75=4 th space
-Count to those positions from the bottom
Calculating the Standard Deviation:
X
18
19
21
X-𝑋̅
(X-𝑋̅)2
-16.33
-15.33
-13.33
266.6689
235.0089
177.6889
Step 1: Calculate each x
values deviation from
the mean
Step 2: Square the
deviations from the
mean
24
28
29
29
29
32
33
33
36
40
44
100
-10.33
-6.33
-5.33
-5.33
-5.33
-2.33
-1.33
-1.33
1.67
5.67
9.67
65.67
106.7089
40.0689
28.4089
28.4089
28.4089
5.4289
1.7689
1.7689
2.7889
32.1489
93.5089
4312.5489
5361.3335
Step 4: Plug sum of
squares into SD formula
𝑆𝐷 = √
(𝑋 − 𝑋̅)2
5361.3335
=√
= √382.9524 = 19.57
𝑛−1
14
SD=19.57 years
Calculate a 95% confidence interval:
1) First, calculate the standard error of the mean.
𝑆𝐷
19.57
19.57
𝑆𝐸𝑀 = =
=
=5.06
√𝑛
√15
3.87
2) Plug in calculated values to the confidence interval formula.
90% CI: 𝑋̅ ± 𝑍𝑐𝑜𝑛𝑓 (𝑆𝐸𝑀 )=34.33±1.95(5.06) = 34.33 ± 9.867 =
(24.463, 44.197)
95% CI: (24.46, 44.20)years
Question 2: The risk of developing iron deficiency is especially high during pregnancy.
Consider the following data on transferrin receptor concentration for a sample of women with
laboratory evidence of overt iron deficiency anemia.
15.2, 9.3, 7.6, 11.9, 10.4, 9.7, 20.4, 9.4, 11.5, 16.2, 9.4, 8.3
a)
b)
c)
d)
Determine the range of data
Determine the median of the data
Calculate the variance of the data
Calculate the standard deviation of the data
Rank order the data first
7.6 8.3 9.3 9.4 9.4 9.7 10.4 11.5 11.9 15.2 16.2 20.4
Sample size n = 12
a) Range = 20.4-7.6 = 12.8
b) Position of median: (n+1)/2= (12+1)/2 = 6.5
Median will an average of 6th and 7th observations in the sorted data.
Median = (9.7+10.4)/2= 10.05
c) Variance s2:
To calculate sample mean X first,
X = (7.6+8.3+….+20.4)/12=11.61
To calculate Standard Deviation and Variance:
X
15.20
9.30
7.60
11.90
10.40
9.70
20.40
9.40
11.50
16.20
9.40
8.30
X- X
3.59
-2.31
-4.01
0.29
-1.21
-1.91
8.79
-2.21
-0.11
4.59
-2.21
-3.31
(X- X )2
12.90
5.33
16.07
0.09
1.46
3.64
77.29
4.88
0.01
21.08
4.88
10.95
158.57
(𝑋−𝑋̅ )2 158.57
a) Variance= 𝑛−1 = 11 = 14.42
b) Standard deviation (SD) s = 14.42 =3.80
Question 3: Match the following variables with the (best fitting) corresponding levels of
Burn Severity:
Nominal
Ordinal
Interval
Ratio
Time:
Nominal
Ordinal
Interval
Ratio
Gender:
Nominal
Ordinal
Interval
Ratio
Question 4: The weight for 3rd grade elementary students in a state is normally distributed with
mean 𝑋̅= 52.3lbs and standard deviation SD=6.2. What is the probability that a 3rd grade student
will weigh at most 40lbs? (SHOW ALL WORK and FORMULAS USED).
𝑧=
𝑋𝑖 − 𝑋̅ 40 − 52.3
=
= −1.98
𝑆𝐷
6.2
Area of
interest
47.615%
Z=-1.98
50%-47.615%=2.385%=.024
The probability that a student will weight at most 40lbs is 0.024.
Question 5: If the probability of event A is P(A)= 0.5 and the probability of a second event B is
P(B) = 0.8, what is the probability of event A happening and then event B happening right after?
a.
b.
c.
d.
0.40
0.06
0.50
There is insufficient information
Question 6: Given below is a 5-point summary of age for 10 women.
Minimum 1st quartile
Median
3rd quartile
Maximum
18
21
29
30
31
The interquartile range for this data set is:
a. 9
b. 8
c. 15
d. 1
IQR=3rd-1st quartile=30-21=9
Question 7: In any normal distribution, the proportion of observations that are within 2
standard deviations of the mean is closest to:
a.
b.
c.
d.
0.9974
0.6826
0.9544
0.9874
Question 8: All of the following are goals of good study design, EXCEPT:
a.
b.
c.
d.
e.
Minimize bias
Evaluate associations between exposures and outcomes
Make inference about a population from a sample
Develop a hypothesis
None of the above
Question 9: You want to collect data about how many steps participants take in a day to assess
their physical activity. You have participants walk on a treadmill for 20 minutes with a device to
measure their step count and also have a research assistant count the number of steps they took.
Why is it s a good idea to have the research assistant count the number of steps if the participant
is wearing a step counting device? [2 points]:
a. To assess the reliability and validity of the step counter
b. To assess the validity of the step counter
c. To assess the reliability of the step counter
d. To assess the research assistants’ ability to count steps
Question 10: Researchers developed a new device to measure body fat % that is inexpensive and
easy to use. Which of the following would be a way to assess reliability of the new device? [2
points]:
a. Compare body fat % from the new device to results from a gold standard
measurement tool
b. Take body fat % from the device one time and record the findings
c. Take body fat % from the same person 5 times using the new device to see if the
device gives similar results every time
d. You can’t assess reliability of a new device
Question 11: Which of the following variables are continuous and which are discrete? Circle
Vocabulary size:
Discrete
Continuous
Reaction time:
Discrete
Continuous
Temperature in Celsius:
Discrete
Continuous
Question 12: You test 75 people for the number of times they could bounce a ping pong ball on
a paddle in 60 seconds. You calculate the mean of your sample to be 30 bounces with a standard
deviation of 13 bounces. Show your work:
𝑋̅=30
sd=13
n=75
a. What is the standard error of the mean?
𝑆𝐸𝑀 =
𝑆𝐷
=
𝑛

13
13
= 8.66 =1.50
75

b. What would be the 95% confidence interval of the predicted ping-pong ball bounces in
a population?
95% CI: 𝑋̅ ± 𝑍𝑐𝑜𝑛𝑓 (𝑆𝐸𝑀 )=30 ± 1.96(1.50) = 30 ± 2.94 =
(27.06, 32.94) bounces
c. If you wanted to compute the 78% confidence interval of population mean, what value
would you use for Z in your equation?
Z=1.22 which corresponds to 38.877% on the z table, the value closest to 39.
Question 13: If we measured data from 5,000 children age 2 to age 10 and found the mean
number of hours spent playing outdoors per week to be 4.8 hours with a standard deviation of 0.5
hours, how many children spent between 4.8 hours and 5.5 hours outdoors per week? Show your
work.
𝑋̅=4.8
SD=0.5
n=5000
X=5.5
𝑧=
𝑋𝑖 − 𝑋̅ 5.5 − 4.8
=
= 1.4
𝑆𝐷
0.5
41.294%
Z=0
𝑋̅ = 4.8
Z=1.4
Multiply area under the curve by the sample size: 0.41294*5000=2064.7
A total of 2065 children spent between 4.8 and 5.5 hours outdoors per week.
Question 14: In a normally distributed population, the mean represents the 50%ile.
A) TRUE
B) FALSE
Question 15: The value for interquartile range is always larger than the range
A) TRUE
B) FALSE
Question 16: A test of tennis serve accuracy resulted in the following data: Note: Higher scores
indicate better performance.
X
15
12
12
10
9
8
8
7
5
4
4
3
a. What is the percentile rank of a person who scored (a) 8; (b) 12?
There are 12 observations
a) 8 is in the 7th position
a. 7/12=.5833*100=58.33 ~59%tile
b) 12 is in the 11th position
a. 11/12=.9167*100=92%tile
b. What is the nearest score to (a) the 70th percentile; (b) the 25th percentile?
a) .70*12=8.4 so you would round to the 9th position for a score of 10
b) .25*12=3rd position for a score of 4
Question 17: What is the probability of choosing a card from a standard deck of cards and
getting either an ace of spades or a seven of any suit? (Note: There are 52 cards in a deck of
cards, 4 suits in each deck (heart, diamond, club, spade), and one card for each suit)
a.
b.
c.
d.
0.039
0.096
0.001
There is insufficient information
Determine probability of getting an ace of spades: 1/52=0.019
Determine probability of seven of any suit: 4/52=0.077
P(A or B)=P(A) +P(B)= P(ACE SPADES)+P(SEVEN OF ANY SUIT)=0.019+0.077=0.096
Question 18: If we measured data from 1500 college students and found the mean number of
hours slept per night to be 5.8 hours with a standard deviation of 0.8 hours, how many college
students would we expect to sleep between 4 and 5 hours? Show your work
𝑋̅=5.8
SD=0.8
n=1500
Step 1: Calculate z score for 4 hours of sleep:
𝑋𝑖 − 𝑋̅ 4 − 5.8
𝑧=
=
= −2.25 𝑜𝑟 𝑗𝑢𝑠𝑡 2.25
𝑆𝐷
0.8
Step 2: Calculate z score for 5 hours of sleep:
𝑋𝑖 − 𝑋̅ 5 − 5.8
𝑧=
=
= −1 𝑜𝑟 𝑗𝑢𝑠𝑡 1
𝑆𝐷
0.8
Step 3: Determine percent under the curve from mean to each z-score calculated
-z-score of 2.25=48.778%
-z-score of 1=34.134%
Step 4: Subtract area between mean and
z score of 1 from area between mean and
z-score of 2.25 to remove area outside of
curve.
48.778-34.134=14.644%
Step 5: Multiply area under curve by
sample size:
0.14644 x 1500=219.66~220
Looking for this
area under the
curve
Z=1
𝑋=5
Z=2.25
𝑋=4
Z=0
𝑋̅ = 5.8
between 4 and 5 hours per night.
Question 19: Download the birthweight.csv data from cougar courses. This dataset contains
information on new born babies and their parents. The data contains the following variables:
Name
Variable
ID
Baby number
length
Birthweight
Gestation
smoker
motherage
mnocig
mheight
mppwt
fage
fedyrs
fnocig
fheight
lowbwt
mage35
Length of baby (cm)
Weight of baby (kg)
Gestation (weeks)
Mother smokes 1 = smoker 0 = non-smoker
Maternal age
Number of cigarettes smoked per day by mother
Mothers height (cm)
Mothers pre-pregnancy weight (kg)
Father’s age
Father’s years in education
Number of cigarettes smoked per day by father
Father’s height (kg)
Low birth weight, 0 = No and 1 = yes
Mother over 35, 0 = No and 1 = yes
Using both JAMOVI and excel answer the following questions.
a. What is the mean, median, standard deviation, and IQR of the following variables:
length, birthweight, motherage, fage, and gestation.
b. In a couple sentences, briefly describe the descriptive statistics you calculated.
KINE 303- Equations
Exam 1
𝑠 ! 𝑜𝑟
∑(𝑋” − 𝑋+)!
𝑉=
𝑛−1
∑(𝑋” − 𝑋+)!
𝑆𝐷 = 1
𝑛−1
𝑋” − 𝑋+
𝑍=
𝑆𝐷
𝜇 = 𝑋+ ± 5𝑍#\$%& 6(𝑆𝐸’ )
𝑆𝐸’ =
𝑆𝐷
√𝑛
Z table
Z
0.00
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.10
0.11
0.12
0.13
0.14
0.15
0.16
0.17
0.18
0.19
0.20
0.21
0.22
0.23
0.24
0.25
0.26
0.27
0.28
0.29
0.30
0.31
0.32
0.33
0.34
0.35
0.36
0.37
0.38
0.39
0.40
0.41
0.42
0.43
0.44
0.45
0.46
0.47
0.48
0.49
Area
0.000%
0.399%
0.798%
1.197%
1.595%
1.994%
2.392%
2.790%
3.188%
3.586%
3.983%
4.380%
4.776%
5.172%
5.567%
5.962%
6.356%
6.749%
7.142%
7.535%
7.926%
8.317%
8.706%
9.095%
9.483%
9.871%
10.257%
10.642%
11.026%
11.409%
11.791%
12.172%
12.552%
12.930%
13.307%
13.683%
14.058%
14.431%
14.803%
15.173%
15.542%
15.910%
16.276%
16.640%
17.003%
17.364%
17.724%
18.082%
18.439%
18.793%
Z
0.50
0.51
0.52
0.53
0.54
0.55
0.56
0.57
0.58
0.59
0.60
0.61
0.62
0.63
0.64
0.65
0.66
0.67
0.68
0.69
0.70
0.71
0.72
0.73
0.74
0.75
0.76
0.77
0.78
0.79
0.80
0.81
0.82
0.83
0.84
0.85
0.86
0.87
0.88
0.89
0.90
0.91
0.92
0.93
0.94
0.95
0.96
0.97
0.98
0.99
Area
19.146%
19.497%
19.847%
20.194%
20.540%
20.884%
21.226%
21.566%
21.904%
22.240%
22.575%
22.907%
23.237%
23.565%
23.891%
24.215%
24.537%
24.857%
25.175%
25.490%
25.804%
26.115%
26.424%
26.730%
27.035%
27.337%
27.637%
27.935%
28.230%
28.524%
28.814%
29.103%
29.389%…
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