Question

In testing the difference between two population means when population standard deviations are

unknown, there are many cases depending upon whether the two population standard deviations

are equal or not. Therefore, before testing the difference between two population means, the

equality of two population variances must be tested first. Let the sample data from population #1

be? =10,?̅ =97.4,? =8.8769andfrompopulation#2be? =7,?̅ =110,? =30.2214. 111 222

Answer the following five questions assuming the level of significance=0.1.

23. In testing the hypothesis ? = ? against ? ≠ ? , the two critical values are 12 12 A) 0.16 & 4.53 B) 0.297 & 4.10 C) 0.21 & 3.97 D) 0.17 & 7.98

24.Continuing 23, the computed statistic is

A) 7.5930 B) 3.4045 C) 0.2937 D) 0.0863

Answer 1

using excel>Addin>phstat>two sample test

we have

F Test for Differences in Two Variances
Data
Level of Significance	0.1
Larger-Variance Sample
Sample Size	10
Sample Standard Deviation	8.8769
Smaller-Variance Sample
Sample Size	7
Sample Standard Deviation	30.2214
Intermediate Calculations
F Test Statistic	0.086277
Population 1 Sample Degrees of Freedom	9
Population 2 Sample Degrees of Freedom	6
lower critical value	0.297
Upper Critical Value	4.1

23. In testing the hypothesis ? = ? against ? ≠ ? , the two critical values are

B) 0.297 & 4.10

24.Continuing 23, the computed statistic is

D) 0.0863