Question 2 - The two sample t test on shingles patients

A pilot study was conducted to evaluate the effectiveness of pain alleviation in patients with facial shingles. 24 patients were randomly assigned to one of 2 treatment groups; rest vs. acupuncture. After two weeks of treatment, the subjects were then asked to rate their pain on a scale from 1 to 10 with 10 being the most pain they have ever experienced. The data they recorded is shown below:

Rest	Acupuncture
5	5
5	6
10	7
9	2
8	9
6	8
9	7
4	4
7	3
8	5
4	9
3	2

Two sample T hypothesis test: ₁: Mean of rest ₂: Mean of acupuncture ₁- ₂: Difference between two means H₀: ₁- ₂= 0 H_A: ₁- ₂ 0 (with pooled variances) Hypothesis test results:

Difference	Sample Diff.	Std. Err.	DF	T-Stat	P-value
1- 2	0.91666667	0.98441132	22	0.93118257	0.3619

1. State the null and alternative hypothesis.

2. What is the value of t for the analysis?

3. Is this value significant and at what level? Why?

4. Why is a pooled variance test allowed here while a separate variance t test is not appropriate?