Chapter 10, Problem 10P

### Essentials of Statistics for the B...

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

Chapter
Section

### Essentials of Statistics for the B...

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

# Two separate samples, receive different treatments. After treatment, the first sample has n = 9 with SS = 462, and the second has n = 7 with SS = 420. a. Compute the pooled variance for the two samples. b. Calculate the estimated standard error for the sample mean difference. c. If the sample mean difference is 10 points, is this enough to reject the null hypothesis using two-tailed test with α = .05?

a.

To determine

To Find: The pooled variance for the two samples of size n1=9 and n2=7

Explanation

Given info:

Two samples with size 9 and 7 have sum of squared difference (SS) equal 462 and 420 respectively.

Calculations:

The degrees of freedom for two samples is:

df1=n11=91=8

Similarly,

df2=n21=71=6

So, the pooled variance, sp2, is calculated using formula:

sp2=

b.

To determine

To Find: The estimated standard error for the sample mean difference.

c.

To determine

To Justify: If we can concludethat there is a significant mean difference using a two-tailed test at α=0.05 for the given question.

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