15.2 A chemical engineer had three different formulas for a gasoline additive that she thought would significantly change automobile gas mileage.

She had three groups of 15 test standard eight-cylinder engines that simulated normal driving conditions. Each group received a different gasoline formulation (A1, A2, and A3) and was run for several hours.

Simulated mileage for the A1 group was 35.60, 34.50, 36.20, 33.10, 36.10, 34.80, 33.90, 34.70, 35.20, 35.80, 36.60, 35.10, 34.90, 36.00, and 34.10. Mileage for A2 was 36.80, 35.30, 37.00, 32.90, 36.80, 35.60, 35.10, 35.80, 36.90, 36.60, 36.80, 36.60, 35.80, 36.30, and 36.00. Mileage for the A3 group was 37.79, 36.29, 38.01, 33.80, 37.79, 36.58, 36.03, 36.79, 37.89, 37.57, 37.79, 37.59, 36.78, 37.29, and 37.01.

Your job is to investigate the mileage numbers in an effort to provide evidence in support of her contention that the groups would have significantly different gas mileage. Write the null and alternative hypotheses. If you find a difference, therefore rejecting the null, you must identify the groups contributing to the significant F statistic with post hoc analysis. Can you provide evidence in support of the chemical engineer’s contention that her formulas will significantly alter gas mileage for these test engines?