Over the past semester youve collected the following data on

Over the past semester, you\'ve collected the following data on the time it takes you to get to school by bus and by car:

• Bus: (15, 10, 7, 13, 14, 9, 8, 12, 15, 10, 13, 13, 8, 10, 12, 11, 14, 11, 9, 12) • Car: (5, 8, 7, 6, 9, 12, 11, 10, 9, 6, 8, 10, 13, 12, 9, 11, 10, 7)

You want to know if there\'s a difference in the time it takes you to get to school by bus and by car.

What test would you use to look for a difference in the two data sets, and what are the conditions for this test? Do the data meet these conditions? Use sketches of modified box-and-whisker plots to support your decision.

What are the degrees of freedom (k) for this test using the conservative method? (Hint: Don\'t pool and don\'t use your calculator.)

What are the sample statistics for this test? Consider the data you collected for bus times to be sample one and the data for car times to be sample two.

Compute a 99% confidence interval for the difference between the time it takes you to get to school on the bus and the time it takes to go by car. Draw a conclusion about this difference based on this confidence interval using Ho : (µ1 - µ2) = 0 as your null.

Solution

The test procedure, called the two-sample t-test, is appropriate when the following conditions are met:

The samples meet the above requirements except that sample size not greater than 40

But as samples are at random we use t test.

H0: mu1 = mu2

Ha: mu1 not equals mu2

Two tailed hypothesis test.

Alpha = 0.01

Df = 18-1 = 17

t value = 2.950

p value = 0.005

Reject null hypothesis

There is significant difference between the two means.