Essentials of Statistics for the Behavioral Sciences
8th Edition
ISBN: 9781133956570
Author: Frederick J Gravetter, Larry B. Wallnau
Publisher: Cengage Learning
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Chapter 7, Problem 19P
At the end of the spring semester, the Dean of Students sent a survey to the entire freshman class. One question asked the students how much weight they had gained or lost since the beginning of the school year. The average was a gain of μ. = 9 pounds with a standard deviation of σ = 6. The distribution of scores was approximately normal. A sample of n = 4 students is selected and the average weight change is computed for the sample.
- a. What is the
probability that the samplemean will be greater than M = 10 pounds? In symbols, what is p(M > 10)? - b. Of all of the possible samples, what proportion will show an average weight loss? In symbols, what is p(M < 0)?
- c. What is the probability that the sample mean will be a gain of between M = 9 and M = 12 pounds? In symbols, what is p(9 < M < 12)?
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West Virginia has one of the highest divorce rates in the nation, with an annual rate of approximately 5 divorces per 1000 people (Centers for Disease Control and Prevention website, January 12, 2012). The Marital Counseling Center, Inc. (MCC) thinks that the high divorce rate in the state may require them to hire additional staff.
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Excel File: data05-19.xls
x
10
f(x)
.05
20
30
.10
.10
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.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
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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
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Number
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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
1120
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.
The input in the box below will not be graded, but may be reviewed and considered by your instructor.
c. What is the probability that a person…
Chapter 7 Solutions
Essentials of Statistics for the Behavioral Sciences
Ch. 7.2 - A population has a mean of = 65 and a standard...Ch. 7.2 - Describe the relationship between the sample size...Ch. 7.2 - For a population with of = 40 and a standard...Ch. 7.3 - A sample is selected from a population with a mean...Ch. 7.3 - What is the probability of obtaining a sample mean...Ch. 7.3 - What are the boundaries for the middle 50% of all...Ch. 7.4 - If a sample is selected from a population with a...Ch. 7.4 - Can the value of the standard error ever be larger...Ch. 7.4 - Prob. 3LCCh. 7.4 - Prob. 4LC
Ch. 7.5 - A population forms a normal distribution with a...Ch. 7.5 - A population forms a normal shaped distribution...Ch. 7.5 - The SAT scores for the entering freshman class at...Ch. 7.5 - Prob. 4LCCh. 7 - Describe the distribution of sample means (shape,...Ch. 7 - A sample is selected from a population with a mean...Ch. 7 - The distribution of sample means is not always a...Ch. 7 - A population has a standard deviation of = 24. a....Ch. 7 - For a population with a mean of = 70 and a...Ch. 7 - For a population with a standard deviation of =...Ch. 7 - For a population with = 12, how large a sample is...Ch. 7 - For a sample of n = 25 scores, what is the value...Ch. 7 - For a population with a mean of = 80 and a...Ch. 7 - A sample of n = 4 scores has a mean of M = 75....Ch. 7 - A normal distribution has a mean of = 60 and a...Ch. 7 - A random sample is obtained from a normal...Ch. 7 - The population of IQ scores forms a normal...Ch. 7 - The scores on a standardized mathematics test for...Ch. 7 - A normal distribution has a mean of = 54 and...Ch. 7 - A population of scores forms a normal distribution...Ch. 7 - For random samples of size n = 25 selected from a...Ch. 7 - The distribution ages for students at the state...Ch. 7 - At the end of the spring semester, the Dean of...Ch. 7 - Jumbo shrimp are those that require 10 to 15...Ch. 7 - The average age for licensed drivers in the county...Ch. 7 - Callahan (2009) conducted a study to evaluate the...Ch. 7 - Xu and Garcia (2008) conducted a research study...
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