Question

Consider the following hypothesis test. H0: μ1 − μ2 = 0 Ha: μ1 − μ2 ≠...

Consider the following hypothesis test.

H0: μ1 − μ2 = 0

Ha: 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.

Homework Answers

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.

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