Question

Consider the following hypothesis test.

H₀: μ₁ − μ₂ = 0

H_a: μ₁ − μ₂ ≠ 0

The following results are from independent samples taken from two populations assuming the variances are unequal.

Sample 1	Sample 2
n1 = 35	n2 = 40
x1 = 13.6	x2 = 10.1
s1 = 5.7	s2 = 8.2

(a) What is the value of the test statistic? (Use x₁ − x₂.  Round your answer to three decimal places.)

(b) What is the degrees of freedom for the t distribution? (Round your answer down to the nearest integer.)

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

p-value =

(d) At α = 0.05, what is your conclusion?

Reject H₀. There is insufficient evidence to conclude that μ₁ − μ₂ ≠ 0.

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

Reject H₀. There is sufficient evidence to conclude that μ₁ − μ₂ ≠ 0.

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

Answer 1

Part a)

Test Statistic :-


t = 2.167

Part b)

DF = 69

Part c)

P - value = P ( t > 2.1667 ) = 0.0337

Looking for the value t = 2.167 in t table across 69 degree of freedom to find the P value.

Part d)

Reject null hypothesis if P value < α = 0.05 level of significance
P - value = 0.0337 < 0.05, hence we reject null hypothesis
Conclusion :- Reject null hypothesis

Reject H₀. There is sufficient evidence to conclude that μ₁ − μ₂ ≠ 0.