Question

n1=37, n2=37, s1= 7.4345, s2= 3.4927, x1= 23.237, x2 = 22.526 Please perform: One Hypothesis test, an F test for the equality of the variances of travel Times and the second test is a T-test for the equality of the means of travel times in MINUTES. The F test must be performed first in order to select either Case1 or Case 2 for the T-test. Then perform the Required T-test (either case 1 or 2 depending on your findings of the F-test). use p value as rejection rule for both tests!!, and use the 5 steps please please help

-the pvalue has to be used as rejection rule, and an f test then a t test (case 1 or 2 depending on f test results). The answers have to be in an interval. Please help me. I need this to review and study. I dont know how to get them in an interval. please make sure the p value is used

Answer 1

For Sample 1 :

x̅1 = 23.237, s1 = 7.4345, n1 = 37

For Sample 2 :

x̅2 = 22.526, s2 = 3.4927, n2 = 37

Null and alternative hypothesis:

Hₒ : σ₁² = σ₂²

H₁ : σ₁² ≠ σ₂²

Test statistic:

F = s₁² / s₂² = 7.4345² / 3.4927² = 4.5309

Degree of freedom:

df₁ = n₁-1 = 36

df₂ = n₂-1 = 36

P-value = 2*F.DIST.RT(4.5309, 36, 36) = 0.0000

p-value < 0.01

Conclusion:

As p-value < α, we reject the null hypothesis.

There is enough evidence to conclude that the variance of these two population are not equal.

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Null and Alternative hypothesis:

Ho : µ1 = µ2

H1 : µ1 ≠ µ2

Test statistic:

t = (x̅1 - x̅2)/√(s1²/n1 + s2²/n2) = (23.237 - 22.526)/√(7.4345²/37 + 3.4927²/37) = 0.5265

df = ((s1²/n1 + s2²/n2)²)/[(s1²/n1)²/(n1-1) + (s2²/n2)²/(n2-1) ] = 51.1529 = 51

p-value =T.DIST.2T(0.5265, 51) = 0.6008

p-value > 0.5

Decision:

p-value > α, Do not reject the null hypothesis

Conclusion:

There is not enough evidence to conclude that the means of these two population are not equal.