Question

The following sample data have been collected from a paired sample from two populations. The claim is that the first population mean will be at least as large as the mean of the second population. This claim will be assumed to be true unless the data strongly suggest otherwise.

Population Data

Sample 1	Sample 2
4.4	3.7
2.7	3.5
1.0	4.0
3.5	4.9
2.8	3.1
2.6	4.2
2.4	5.2
2.0	4.4
2.8	4.3

1. State the appropriate null and alternative hypotheses.
2. Based on the sample data, what should you conclude about the null hypothesis? Test using α = 0.10.

Answer 1

From above probability plot, we see that assumption of normality holds.

Test and CI for Two Variances: Sample 1, Sample 2

Method

Null hypothesis         Variance(Sample 1) / Variance(Sample 2) = 1
Alternative hypothesis Variance(Sample 1) / Variance(Sample 2) not = 1
Significance level      Alpha = 0.05

Statistics

Variable N StDev Variance
Sample 1 9 0.937     0.879
Sample 2 9 0.662     0.438

Ratio of standard deviations = 1.417
Ratio of variances = 2.007

                                                       Test

Method                          DF1 DF2 Statistic P-Value
F Test (normal)                   8    8       2.01    0.344

Since P-value>0.1 so we can assume the two population variances are same.