Question

Given the computer output shown following for testing the hypotheses

                                    H_o: (μ₁ - μ₂) = 0

                                    H_a: (μ₁ - μ₂) > 0

            What conclusion would you draw, with α = .10? What assumption(s) did you make in      answering this question?

            Variable: X

SAMPLE	N	Mean	Std Dev	Std Error
1	32	77.1	6.03	1.07
2	58	75.2	4.21	0.55

Variances	T	DF	Prob > ∣T∣
Unequal	1.58	48.0	0.1206
Equal	1.74	88.0	0.0848

Answer 1

Answer:

This is two sample t -test

The Assumptions of the two-sample t-test are:

1. The data are continuous (not discrete).

2. The data follow the normal probability distribution.

3. The variances of the two populations are equal. (If not, the Aspin-Welch Unequal-Variance test is used.)

4. The two samples are independent. There is no relationship between the individuals in one sample as compared to the other (as there is in the paired t-test).

5. Both samples are simple random samples from their respective populations. Each individual in the population has an equal probability of being selected in the sample.

Here the output is given for both types that is for unequal variance and assuming equal variance.

α = 0.10, and we know that if p-value( i.e prob > |t| ) is less than α = 0.10 then we reject Ho .

By assuming 3rd assumption above from output, when Assuming equal variance the p-value = 0.0848 < α = 0.10 hence we reject Ho .

But if use p-value of unequal variances then p-value = 0.1206 > α = 0.10 then we do not reject Ho .