3. Dr. Michaella Evans, a statistics professor at the University of Maryland University College, drives from her home to the school every weekday. She has three options to drive there. She can take the Beltway, or she can take a main highway with some traffic lights, or she can take the back road, which has no traffic lights but is a longer distance. Being as data-oriented as she is, she is interested to know if there is a difference in the time it takes to drive each route.
As an experiment she randomly selected the route on 21 different days and wrote down the time it took her for the round trip, getting to work in the morning and back home in the evening. At the .01 significance level, can she conclude that there is a difference between the driving times using the different routes?

Beltway Main highway Back road 88 79 86 94 86 78 91 75 79 88 83 96 98 74 97 84 72 73 90 68 77 Step 1: State the null hypothesis and the alternate hypothesis
"Ho: The population mean driving times of the three routes are statistically equal.
H1: At least one of the population mean driving times does not equal one of the other population group means
"

Step 2: Select the level of significance
The level of significance is .01 Step 3: Determine the test statistic
The Analysis of Variance procedure is chosen because we are testing to see if more than 2 population means are statistically equivalent. The ANOVA is based on the F-distribution.
Note that the F-distribution is a three dimension table. There are three variables required to obtain the critical value: The level of significance, the degrees of freedom in the numerator and the degrees of freedom in the denominator.
(Note the ANOVA always uses a nondirectional alternative