test1reviewanswers
pdf
keyboard_arrow_up
School
Tunxis Community College *
*We aren’t endorsed by this school
Course
MAT*137
Subject
Mathematics
Date
Jan 9, 2024
Type
Pages
6
Uploaded by MinisterHedgehogPerson922
MAT 167: Principles of Statistics
Test 1 Review Answers
Practice Questions
1. A study followed 250 college seniors for 15 years after graduation. After 15 years, the median salary
of the 250 graduates was
62,000 per year.
(a) Identify the population and the sample involved in this study.
The sample is the 250 college seniors. The population is all college graduates.
(b) Determine whether the median salary mentioned is a parameter or a statistic.
The median salary is a statistic because it is sample data.
(c) Determine whether the variable “salary” is qualitative or quantitative.
This is a quantitative variable.
(d) If “salary” is a quantitative variable, determine whether it is a discrete or continuous variable.
This is a continuous variable.
2. Researchers want to determine if gender has an effect on driving safety. They follow a random sample
of drivers age 16 to age 90 for a year and collect data on how many accidents each driver was involved
in during that year.
(a) Is this an observational study or an experiment? Why?
This is an observational study because the researchers are not controlling the variables, only
observing what happens.
(b) What is the response variable? What is the explanatory variable?
The response variable is driving safety. The explanatory variable is gender.
(c) What are some potential confounding variables that the researchers should take into account?
Age of the driver, health conditions the driver may have, how much training the driver has had
(there may be others)
3. The CEO of a company wants to have lunch with a random sample of 5 employees to hear their
concerns. The company employs 20 people: Anthony, Becky, Brian, Chantelle, Devin, Ezra, Felicia,
Hector, Joan, Julissa, Kobe, Mark, Noblesse, Noemi, Quetzali, Shawn, Temira, Thomas, Victor,
Yeika. Use the table of random numbers below to select a simple random sample of 5 employees to
have lunch with the CEO.
24388 71647 78231 74394 31438 44587 42039 42304 71943 11043 84832 41307 65614 62339 49371
Brian, Chantelle, Julissa, Shawn, and Temira are chosen.
4. A researcher wants to obtain a random sample of 40 Connecticut residents for a study.
She first
separates the population by county. Then she uses simple random sampling to select 5 individuals
from each county. What type of random sampling is this?
This is stratified sampling.
5. A sample of 20 American adults were asked how much they spend on coffee per day. Given the data
set below, answer the following questions.
7.49,
2.98,
1.97,
0.00,
2.19,
2.05,
0.00,
1.85,
3.79,
1.75,
1.99,
2.37,
2.51,
1.19,
1.65,
3.07,
2.98,
1.69,
1.99,
0.00
(a) Construct an expanded frequency distribution with 4 classes (find the lower and upper class
limits, the frequencies, the relative frequencies, and the cumulative frequencies)
Classes
Frequency
Relative Frequency
Cumulative Frequency
0-1.99
11
0.55
11
2-3.99
8
0.4
19
4-5.99
0
0
19
6-7.99
1
0.05
20
(b) Construct a histogram of the data. Do there appear to be any outliers? What is the shape of
the distribution? What does that tell you about the mean and median?
It looks like
7.49 is an outlier. The data is slightly skewed right. Therefore we would expect
that the mean is greater than the median.
(c) Compute the mean, median, mode, and range of the data by hand.
x
≈
2
.
18,
M
= 1
.
99, modes= 1
.
99
,
2
.
98,
R
= 7
.
49.
(d) Construct a stem-and-leaf plot of the data.
0.0
000
1.0
1.1
9
1.2
1.3
1.4
1.5
1.6
59
1.7
5
1.8
5
1.9
799
2.0
5
2.1
9
2.2
2.3
7
2.4
2.5
1
2.6
2.7
2.8
2.9
88
3.0
7
3.1
3.2
3.3
3.4
3.5
3.6
3.7
9
3.8
3.9
.
.
.
.
.
.
7.0
7.1
7.2
7.3
7.4
9
7.5
7.6
7.7
7.8
7.9
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
(e) Construct a frequency ogive of the data.
(f) Find the 5-number summary and IQR.
5-number summary: 0, 1.67, 1.99, 2.745, 7.49. IQR= 1
.
075
(g) Find the upper and lower fences and construct a boxplot of the data. Are there any outliers?
UF= 4
.
3575, LF= 0
.
0575. The three 0s and the 7.49 are outliers.
(h) Compute the standard deviation of the data by hand.
s
≈
1
.
609
(i) Estimate the mean from the frequency distribution.
x
≈
2
.
1
6. 20 people were asked how many cups of coffee they drink per day. The results were:
7, 2, 1, 0, 2, 2, 0, 1, 3, 1, 1, 2, 2, 1, 1, 3, 2, 1, 1, 0
Make a dotplot of this data.
7. The lunch break lengths (in minutes) for employees of a certain company form a bell-shaped distri-
bution with a mean of 31 minutes and a standard deviation of 4 minutes. You would expect 95% of
the lunch break lengths to fall between what two lengths?
Since this is a bell-shaped distribution, we can use the Empirical Rule, which says that approximately
95% of the data falls within 2 standard deviations of the mean. So we expect that 95% of the lunch
break lengths will fall between 23 and 39 minutes.
Formulas
1.
s
=
r
Σ(
x
i
-
x
)
2
n
-
1
2.
x
=
Σ
x
i
f
i
Σ
f
i
3. LF=
Q
1
-
1
.
5IQR
4. UF=
Q
3
+ 1
.
5IQR
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help