Question

Suppose we have taken independent, random samples of sizes n₁ = 7 and n₂ = 8 from two normally distributed populations having means µ₁ and µ₂, and suppose we obtain x¯1  = 229x¯1⁢  = 229, x¯2  =  190x¯2⁢  =⁢  190, s₁ = 6, s₂ = 6. Use critical values to test the null hypothesis H₀: µ₁ − µ₂ < 28 versus the alternative hypothesis H_a: µ₁ − µ₂ > 28 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 28? (Round your answer to 3 decimal places.)

  t =

  (Click to select)Do not rejectReject H₀ at α = 0.1, 0.05, and, 0.01, (Click to select)weaknoVery strongExtremely strongstrong  evidence.

Answer 1

Ho:μ1-μ2	=	28
Ha: μ1-μ2	<	28

	A	B
sample mean x =	229.00	190.00
standard deviation s=	6.000	6.000
sample size n=	7	8
Pooled Variance Sp2=((n1-1)s21+(n2-1)*s22)/(n1+n2-2)=			36.0000
Pooled Std dev Sp=√((n1-1)s21+(n2-1)*s22)/(n1+n2-2)=			6.00
Point estimate : x1-x2=		39.0000
std. error se =Sp*√(1/n1+1/n2)=		3.1053
test stat t =(x1-x2-Δo)/Se=		3.542

Do not reject at α = 0.1, 0.05, and, 0.01,

no evidence (Since sample difference >28)