Question

In Exercises a-c, test the claim about the difference between two population means μ1 and μ2 at the level of significance α. Assume the samples are random and independent, and the populations are normally distributed.

a. Claim: μ1 = μ2; α = 0.05. Assume

Sample statistics: , X1=228, s1 = 27, n1 = 20 and X2=207, s2 = 25, n2 = 13

b.Claim: μ1 ≤ μ2; α = 0.10. Assume

Sample statistics: , X1=664.5, s1 = 2.4, n1 = 40 and X2=665.5, s2 = 4.1, n2 = 40

c. Claim: μ1 ≥ μ2; α = 0.01. Assume

Sample statistics: X1= 44.5 , s₁ = 5.85, n₁ = 17 and X2= 49.1, s₂ = 5.25, n₂ = 18

Answer 1

a) H0: μ1 = μ2
   H1: μ1 not = μ2
Let the los be alpha = 5%

Critical t:        ±2.039511
P-Value:           0.0140

Here t value is not in t critical values and P-value < alpha 0.05 so we reject H0

Thus we conclude that μ1 not = μ2

b) H0: μ1 = μ2

H1: μ1 ≤ μ2

Let the los be alpha = 5%

Test Statistic, t: -1.3313
Critical t:        -1.292501
P-Value:           0.0935

Here t value < t critical value and P-value < 0.01 so we reject H0

Thus we conclude that μ1 ≤ μ2

c) H0: μ1 = μ2

H1: μ1 ≥ μ2

Let the los be alpha = 5%

Critical t:        2.444792
P-Value:           0.9901

Here t value < t critical value and P-value > alpha 0.01 so we accept H0

Thus we conclude that μ1 = μ2