Fast Food Dinner Service Times Data Set 25 “Fast Food” in Appendix B lists drivethrough service times (seconds) for dinners at McDonald’s, Burger King, and Wendy’s. Using those times with a TI-83>84 Plus calculator yields the following display. Using a 0.05 significance level, test the claim that the three samples are from populations with the same mean. What do you conclude?

Drive-through service times for dinners at three places are compared.

The level of significance is 0.05.

Let\[{\mu _1},{\mu _2},{\mu _3}\]be the actual mean service times for McDonald’s, Burger King, and Wendy’s, respectively.

The hypotheses are stated below.

\(\begin{array}{l}{H_0}:{\mu _1} = {\mu _2} = {\mu _3}\\{H_a}:\;{\rm{at}}\;{\rm{least}}\;{\rm{one}}\;{\mu _i}\;{\rm{is}}\;{\rm{different}}{\rm{.}}\end{array}\)

Decision rule:

• For a p-value less than 0.05, the null hypothesis is rejected.
• For a p-value greater than 0.05, the null hypothesis is failed to be rejected.

From the output of the TI-83/84 Plus calculator, the p-value is marked as\(P = 0.0045462237\). It is lesser than 0.05. Thus, the null is rejected at the 0.05 significance level.

Rejecting the null hypothesis implies that the mean service time for at least one of the three dinners is statistically different from the others. As a result, it can be concluded that the populations from which three samples have been selected have varying mean time.