Question

A comparison is made between two bus lines to determine if arrival times of their regular buses from Denver to Durango are off schedule by the same amount of time. For 51 randomly selected runs, bus line A was observed to be off schedule an average time of 53 minutes, with standard deviation 19 minutes. For 60 randomly selected runs, bus line B was observed to be off schedule an average of 62 minutes, with standard deviation 15 minutes. Do the data indicate a significant difference in average off-schedule times? Use a 5% level of significance.

Answer 1

The test hypothesis is

This is a two-sided test because the alternative hypothesis is formulated to detect differences from the hypothesized difference in mean values on either side.
Now, the value of test static can be found out by following formula:

Degrees of freedom on the t-test statistic are n1 + n2 - 2 = 51 + 60 - 2 = 109
For . Since , we reject the null hypothesis H0 in favor of the alternative hypothesis .
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