Question

Suppose we have taken independent, random samples of sizes n₁ = 7 and n₂ = 7 from two normally distributed populations having means µ₁ and µ₂, and suppose we obtain x⎯⎯1= 240x¯1⁢  = 240 , x⎯⎯2=210x¯2⁢  =⁢  210 , s₁ = 5, s₂ = 6. Use critical values to test the null hypothesis H₀: µ₁− µ₂ < 20 versus the alternative hypothesis H_a: µ₁ − µ₂ > 20 by setting α equal to .10, .05, .01 and .001. Using the equal variance procedure, how much evidence is there that the difference between µ₁ and µ₂ exceeds 20? (Round your answer to 3 decimal places.)

t=

Answer 1

Given H₀: µ₁− µ₂ < 20 versus the alternative hypothesis H_a: µ₁ − µ₂ > 20

Test Statistic, t: 3.3875
Critical t: 1.782286
P-Value: 0.0027

since t value > t critical value and P-value is < alpha 0.10, 0.05, 0.01 so we reject H0

Thus we conclude that µ₁ − µ₂ > 20

If alpha = 0.001

since p-value > alpha 0.001 so we accept H0

Thus we conclude that µ₁− µ₂ < 20