Introduction to Statistics and Data Analysis
5th Edition
ISBN: 9781305115347
Author: Roxy Peck; Chris Olsen; Jay L. Devore
Publisher: Brooks Cole
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Chapter 2.2, Problem 29E
The financial aid advisor of a university plans to use a stratified random sample to estimate the average amount of money that students spend on textbooks each term. For each of the following proposed stratification schemes, discuss whether it would be worthwhile to stratify the university students in this manner. (Hint: Remember that it is desirable to create strata that are homogeneous.)
- a. Strata corresponding to class standing (freshman, sophomore, junior, senior, graduate student)
- b. Strata corresponding to field of study, using the following categories: engineering, architecture, business, other
- c. Strata corresponding to the first letter of the last name: A–E, F–K, etc.
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Excel File: data05-19.xls
x
10
f(x)
.05
20
30
.10
.10
40
.20
50
60
.35
.20
a. Is this probability distribution valid?
- Select your answer-
Explain.
f(x)
Σf(x)
Select your answer
Select your answer
b. What is the probability MCC will obtain more than 30 new clients (to 2 decimals)?
c. What is the probability MCC will obtain fewer than 20 new clients (to 2 decimals)?
d. Compute the expected value and variance of x.
Expected value
Variance
clients per year
squared clients per year
For unemployed persons in the United States, the average number of months of unemployment at the end of December 2009 was approximately seven months (Bureau of Labor Statistics, January 2010). Suppose the following data are for a particular region in upstate New York. The values in the first column show the number of
months unemployed and the values in the second column show the corresponding number of unemployed persons.
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1
1029
2
1686
3
2269
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2675
5
3487
6
4652
7
4145
8
3587
9
2325
10
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Let x be a random variable indicating the number of months a person is unemployed.
a. Use the data to develop an empirical discrete probability distribution for x (to 4 decimals).
(x)
f(x)
1
2
3
4
5
6
7
8
9
10
b. Show that your probability distribution satisfies the conditions for a valid discrete probability distribution.
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Introduction to Statistics and Data Analysis
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