Answer:
a) We reject H₀ We find difference between the mean of the two groups
b) we accept H₀ : There is no statistical difference ( in the scale of pain) when the difference in samples means is 1
Step-by-step explanation:
Group 1: Only with educational material
Sample size n₁ = 42
Sample mean x₁ = 3,2
Sample standard deviation s₁ = 2,3
Group 2: With exercises with the treatment of individuals
Sample size n₂ = 42
Sample mean x₂ = 5,2
Sample standard deviation s₂ = 2,3
Test Hypothesis
Null Hypothesis H₀ x₂ - x₁ = 0 or x₁ = x₂
Alternative Hypothesis Hₐ x₂ - x ₁ > 0 or x₂ > x₁
Significance level α = 0,01
Sample sizes are n₁ = n₂ > 30
We use z-test
for α = 0,01 z(c) ≈ 2,32
To calculate z(s)
z(s) = ( x₂ - x₁ ) / √ (2,3)²/42 + (2,3)²/42
z(s) = ( 5,2 - 3,2 )/ √0,2519
z(s) = 2 / 0,5
z(s) = 4
Comparing z(s) and z(c)
z(s) > z(c)
z(s) is in the rejection region. We reject H₀ the true average pain level for the control condition exceeds that for the treatment condition.
b) Does the true average pain level for the control condition exceed that for the treatment condition by more than 1.
In this case
z( s) = x₂ - x₁ / 0,5
z(s) = 1 /0,5
z(s) = 2
Comparing z(s) and z(c) now
z(s) < z(c) 2 < 2,32
And z(s) is in the acceptance region ( for the same significance level) and we should accept H₀ equivalent to say that the two groups statistical have the same mean
