   Chapter 10, Problem 12P Essentials of Statistics for the B...

8th Edition
Frederick J Gravetter + 1 other
ISBN: 9781133956570

Solutions

Chapter
Section Essentials of Statistics for the B...

8th Edition
Frederick J Gravetter + 1 other
ISBN: 9781133956570
Textbook Problem

For each of the following, calculate the pooled variance and the estimated standard error for the sample mean difference. a. The first sample has n = 4 scores and a variance of s2 = 55, and the second sample has n = 6 scores and a variance of s2 = 63. b. Now the sample variances are increased so that the first sample has n = 4 scores and a variance of s2 = 220, and the second sample has n = 6 scores and a variance of s2 = 252. c. Comparing your answers for parts a and b, how does increased variance influence the size of the estimated standard error?

a.

To determine

To Find: The estimated standard error for the given question

Explanation

Given info:

Two samples with size 4 and 6 have variance 55 and 63 respectively.

Calculations:

The degrees of freedom for two samples is:

df1=n11=41=3

Similarly,

df2=n21=61=5

The pooled variance can be calculated using formula

sp2=(df1)s12+(df2)s22df1+df2

Substitute 55 for s12, 63 for s22, 3 for df1 and 5 for df2 in the above formula

sp2=

b.

To determine

To Find: The estimated standard error for the given question.

c.

To determine

To Describe: Increased variance influence the size of the estimated standard error.

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