SOLUTIONS
MAT 167: Statistics
Test II
Instructor: Anthony Tanbakuchi
Spring 2008
Name:
Computer / Seat Number:
No books, notes, or friends.
Show your work.
You may use the attached
equation sheet, R, and a calculator. No other materials. If you choose to use R,
write what you typed on the test or copy and paste your work into a word
document labeling the question number it corresponds to. When you are done
with the test print out the document. Be sure to save often on a memory stick just
in case. Using any other program or having any other documents open on the
computer will constitute cheating.
You have until the end of class to finish the exam, manage your time wisely.
If something is unclear quietly come up and ask me.
If the question is legitimate I will inform the whole class.
Express all final answers to 3 significant digits. Probabilities should be given as a
decimal number unless a percent is requested. Circle final answers, ambiguous or
multiple answers will not be accepted. Show steps where appropriate.
The exam consists of 13 questions for a total of 84 points on 12 pages.
This Exam is being given under the guidelines of our institution’s
Code of Academic Ethics
. You are expected to respect those guidelines.
Points Earned:
out of 84 total points
Exam Score:
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MAT 167: Statistics, Test II
SOLUTIONS p. 1 of 12
Solution:
Spring 2008 results. I made the exam out of 82 points instead of 84.
>
summary( score )
Min .
1 st
Qu.
Median
Mean 3rd Qu.
Max.
43.29
68.60
81.10
75.75
89.79
95.12
>
par (mfrow = c (1 ,
2))
>
boxplot ( score ,
main = ”Boxplot
of
exam
scores ”)
>
h i s t ( score ,
main = ”Histogram
of
exam
scores ”)
50
60
70
80
90
Boxplot of exam scores
Histogram of exam scores
score
Frequency
40
50
60
70
80
90
0
1
2
3
4
5
6
1. An experiment consists of randomly sampling 10 students at Pima Community College, record
ing their heights and computing their mean height. If we repeat the experiment over and over
(assume simple random samples, no human errors, no bias) we observe that the sample mean
height varies each time.
(a) (2 points) What is the name of the error that causes the mean to vary each time?
Solution:
sampling error
(b) (2 points) Explain how it is possible for the sample mean height to vary each time? What
is going on?
Solution:
Each time we conduct a random sample of size
n
from a fixed population,
the elements that are selected in the sample will vary. Since the samples vary then we
would expect the sample mean to vary as well. This is the natural variation we would
expect to see from sample to sample called sampling error.
(c) (2 points) In words, state what the population distribution represents in this experiment.
(Be specific.)
Solution:
A population distribution describes the distribution of population values.
In this experiment, the population distribution describes the heights of all students at
Pima Community College.
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 Spring '11
 Tanbakuchi
 Statistics, Normal Distribution, Anthony Tanbakuchi

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