Question

The objective of the question is to test the Hypothesis If the Mean travel time in minutes between Point A to Point B is equal to the mean of the travel time in minutes from Point B to your A. First you must find the mean and standard deviations. Then perform and list the complete required steps for the TWO required Hypothesis tests and use the P-Value as a rejection Rule for both tests.

One Hypothesis test is 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.

Recorded Time values in minutes from point A to point B in minutes: 32, 34, 51, 30, 29, 35, 36, 29, 32, 29, 33, 32, 29, 30, 33, 30, 30, 33, 30, 31, 35, 35, 34, 33, 31, 34, 30, 30, 29, 34, 32, 35, 29, 30, 32, 30, 33, 31

n_A=38

Recorded Time values in minutes from point B to point A in minutes: 36, 28, 48, 28, 27, 54, 34, 29, 26, 34, 33, 42, 29, 34, 31, 4, 27, 42, 28, 45, 26, 43, 32, 30, 27, 29, 29, 35, 26, 31, 28, 27, 28, 32, 41, 34, 28, 31

n_B=38

Answer 1

n1 = 38

= 32.2368

s1 = 3.7664

n2 = 38

= 32

s2 = 8.1936

Claim: the Mean travel time in minutes between Point A to Point B is equal to the mean of the travel time in minutes from Point B to your A.

The null and alternative hypothesis is

For doing this test first we have to check the two groups have population variances are equal or not.

Null and alternative hypothesis is

Test statistic is

F = largest sample variance / Smallest sample variances

F = 8.1936^2 / 3.7664^2 = 4.73

Degrees of freedom => n1 - 1 , n2 - 1 => 38 - 1 , 38 - 1 => 37 , 37

Critical value = 1.730 ( Using f table)

Critical value < test statistic so we reject null hypothesis.

Conclusion: The population variances are NOT equal.

So we cant use here pooled variance.

Test statistic is

P-value = 2*P(T > 0.16) = 0.8720

P-value > 0.05 we fail to reject the null hypothesis.

Conclusion:

The Arby sandwich has fewer calories than the MacDonald sandwich.

Conclusion: the Mean travel time in minutes between Point A to Point B is equal to the mean of the travel time in minutes from Point B to your A.