   Chapter 4, Problem 17P Statistics for The Behavioral Scie...

10th Edition
Frederick J Gravetter + 1 other
ISBN: 9781305504912

Solutions

Chapter
Section Statistics for The Behavioral Scie...

10th Edition
Frederick J Gravetter + 1 other
ISBN: 9781305504912
Textbook Problem

For the following sample of n = 8 scores: 0, 1, ½, 0, 3, ½, 0, and 1: Simp1ify the arithmetic by first multiplying each score by 2 to obtain a new sample of 0, 2, 1, 0, 6, 0 and 2. Then, compute the mean and standarddeviation for the new sample.Using the value you obtained in part a, what are the values for the mean and standard deviation for the original sample?

To determine

Mean and standard deviation of a new converted sample and using the result of new sample we need to find the mean standard deviation of old sample

Explanation

Here we have to find the first mean then variance and followed by SD. So, in the calculation part will see how each step has done. And for part b will use part a and the sample values will be half of that and the statistic mean, and SD will follow from this only.

Given:

Here y=0, 1, 0.5, 0, 3, 0.5,0,1 and n=8, samples are given

Formula Used:

For sample of size n, we have below formulas

Mean= x ¯ = 1 n i=1 n x i

Variance= 1 n1 i=1 n ( x i x ¯ ) 2

Standard Deviation (SD)= 1 n1 i=1 n ( x i x ¯ ) 2

[we know the properties of mean and Variance

Define,

Y=X+b

Z=a*X

To find the mean and Variance of Y and Z

Where X having mean m and Variance s2

E(Y) =E (X +b) =E(X) +b=m+b; var(Y) =Var(X) = s2

E(z)=a*E(X)=a*m; Var(Z)=var(X)*a2= s2*a2

Here a and b are arbitrary constant]

Calculation:

a)

 Y X=2*y (x- x ¯ )2 0 0 2.25 1 2 0.25 0.5 1 0.25 0 0 2.25 3 6 20.25 0.5 1 0.25 0 0 2

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