Bundle: Essentials of Statistics for The Behavioral Sciences, Loose-Leaf Version, 9th + Aplia, 1 term Printed Access Card
Bundle: Essentials of Statistics for The Behavioral Sciences, Loose-Leaf Version, 9th + Aplia, 1 term Printed Access Card
9th Edition
ISBN: 9781337593830
Author: Frederick J Gravetter, Larry B. Wallnau, Lori-Ann B. Forzano
Publisher: Cengage Learning
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Textbook Question
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Chapter 5, Problem 24P

A population consists of the following N – 6 scores: 2, 4, 1, 2, 7, 2

  1. a. Compute μ and σ for the population.
  2. b. Find the z-score for each score in the population.
  3. c. Transform the original population into a new population of N = 5 scores with a mean of μ = 50 and a standard deviation of σ = 10.

(a)

Expert Solution
Check Mark
To determine

To Find: The mean and standard deviation for the population scores.

Answer to Problem 24P

The mean and standard deviation for the population scores is 3 and 2.

Explanation of Solution

Given info:

The population consists of the score is, 2, 4, 1, 2, 7, and 2.

Calculation:

The formula for calculating the population mean is,

μ=xiN

The formula for calculating the population standard deviation is,

σ=(xμ)2N

The population mean is,

μ=xiN=2+4+1+2+7+26=186=3

The population standard deviation is,

σ=(xμ)2N=(23)2+(43)2+(13)2+(23)2+(73)2+(23)26=4=2

Conclusion:

Therefore, the required population mean and standard deviation are 3 and 2.

(b)

Expert Solution
Check Mark
To determine

To Find: The z-score for each score in the population.

Answer to Problem 24P

The z-score for each score in the population is,

X- score z -score
2 –0.5
4 0.5
1 –1
2 –0.5
7 2
2 –0.5

Explanation of Solution

Given Info:

The population has mean μ=3 and standard deviation σ=2.

Calculation:

The formula for calculating the z-score is,

z=Xμσ

The z-score corresponding to X score 2 is,

z=Xμσ=232=0.50

The z-score corresponding to X score 4 is,

z=Xμσ=432=0.50

The z-score corresponding to X score 1 is,

z=Xμσ=132=1.00

The z-score corresponding X score 2 is,

z=Xμσ=232=0.50

The z-score corresponding X score 7 is,

z=Xμσ=732=2.00

The z-score corresponding X score 2 is,

z=Xμσ=232=0.50

Conclusion:

The required z-score for each score in the population is,

X- score z-score
2 –0.5
4 0.5
1 –1
2 –0.5
7 2
2 –0.5

(c)

Expert Solution
Check Mark
To determine

To find: Transform original population in to new population with mean μ=50 and standard deviation σ=10.

Answer to Problem 24P

The transformed original population in to new population is,

Original X-score z-score Transformed X
2 –0.5 45
4 0.5 55
1 –1 40
2 –0.5 45
7 2 70
2 –0.5 45

Explanation of Solution

Given Info:

The sample has mean μ=50 and standard deviation σ=10.

Calculation:

The formula for transform original population in to new population is,

X=μ+z×σ

The original population value 2 is transfer into a new population is,

X=μ+z×σ=50+(0.50)×10=45

The original population value 4 is transfer into a new population is,

X=μ+z×σ=50+(0.50)×10=55

The original population value 1 is transfer into a new population is,

X=μ+z×σ=50+(1.00)×10=40

The original population value 2 is transfer into a new population is,

X=μ+z×σ=50+(0.50)×10=45

The original population value 7 is transfer into a new population is,

X=μ+z×σ=50+(2.00)×10=70

The original population value 2 is transfer into a new population is,

X=μ+z×σ=50+(0.50)×10=45

Conclusion:

Thus, the below table shows the transformed original population in to new population:

Original X-score z-score Transformed X
2 –0.5 45
4 0.5 55
1 –1 40
2 –0.5 45
7 2 70
2 –0.5 45

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Chapter 5 Solutions

Bundle: Essentials of Statistics for The Behavioral Sciences, Loose-Leaf Version, 9th + Aplia, 1 term Printed Access Card

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