Question

Consider the following hypothesis test.

H₀: μ₁ − μ₂ ≤ 0

H_a: μ₁ − μ₂ > 0

The following results are for two independent samples taken from the two populations.

Sample 1	Sample 2
n1 = 40	n2 = 50
x1 = 25.7	x2 = 22.8
σ1 = 5.7	σ2 = 6

(a)

What is the value of the test statistic? (Round your answer to two decimal places.)

(b)

What is the p-value? (Round your answer to four decimal places.)

(c)

With

α = 0.05,

what is your hypothesis testing conclusion?

Reject H₀. There is sufficient evidence to conclude that μ₁ − μ₂ > 0. Reject H₀. There is insufficient evidence to conclude that μ₁ − μ₂ > 0.      Do not Reject H₀. There is sufficient evidence to conclude that μ₁ − μ₂ > 0. Do not reject H₀. There is insufficient evidence to conclude that μ₁ − μ₂ > 0.

Answer 1

a) test statistic

Z = (x1bar - x2bar)/sqrt [ 12/n1 + 22/n2 ]

Z = ( 25.7 -22.8)/sqrt[ 5.72/40 + 62/50]

Z = 1.89

b) For Z = 1.89 and right tailed test

p-value = P ( Z > 1.89)

p-value = 0.0294

c) if p-value < a we reject the null hypothesis otherwise we fail to reject the null hypothesis

our p-value = 0.0294 < 0.05

Conclusion : Reject Ho  There is sufficient evidence to conclude that μ1 − μ2 > 0