   Chapter 12, Problem 20P 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

The following values summarize the results from an independent-measures study comparing two treatment conditions.a. Use an independent-measures t test with α = .05 to determine whether there is a significant mean difference between the two treatments. You should find that F = t2.b. Use an ANOVA with α = .05 to determine whether there is a significant mean difference between the two treatments. a.

To determine
Whether there in a significant mean difference between the two treatments using t test.

Explanation

Given info:

From a study of independent measures for comparing two treatments,

 Treatment 1 Treatment 2 N=12G=72∑X2=588 n=8 n=4 M=4 M=10 T=32 T=40 SS=45 SS=15

Calculation:

The null and alternative hypotheses:

Null hypothesis:

H0:There is no significant difference between the two treatments

Alternate hypothesis:

Ha:There is significant different between the two treatments

Degrees of freedom:

It is known that for k number of treatments the degrees of freedom is,

df=n1+n22.

Thus,

df=n1+n22=8+42=10

Critical value:

From t-distribution table, with α=0.05 and df=10, the critical value is ±2.228

Pooled variance:

The pooled variance is sp2=SS1+SS2df1+df2.

Thus,

sp2=SS1+SS2df1+df2=45+157+3=6

Estimated standard error:

The estimated standard error is sM1-M2=sp2n1+sp2n2

b.

To determine
Whether there is a significant mean difference between the two treatments using ANOVA at α=0.05.

To check: Fratio=t2

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