Question

Problem Home products Inc. is considering marketing a long-lasting car wax. Three different waxes (Type 1, Type 2, and Type 3) have been developed. Are the three waxes equally effective? Be prepared to answer any questions concerning this problem In order to test the durability of these waxes, 5 new cars were waxed with Type 1, 5 with Type 2, and 5 with Type 3 Each car was then repeatedly run through an automatic carwash until the wax coating showed signs of deterioration. The number of times each car went through the carwash is shown below. The design is randomized two factors of car type and type of wax. Discussion was to make sure that we replicate the design and block on different cars, because the car type and time may have a different effect that cannot be controlled Are the three waxes equally effective? Be prepared to answer any questions concerning this problem. # of washings 1Wax Type Wax Type 1 2 Wax Mustang 27 Mustang28 30 29 29 28 Challenger 28 Challenger 29 30 31 Type 28 29 31 31 30 30 30 30 31 31 28 27 Camaro Camaro Viper Viper 30 29 30 30 31 30 32 T Bird T Bird

Find the calculated test statistic, critical value, and critical value of P

Answer 1

Two-way ANOVA: C1 versus Wax Type, Car

Source DF SS MS F P-value Critical value
Wax Type 2 8.8667 4.43333 6.05 0.012 F_0.05,2,15=3.6823
Car 4 35.0000 8.75000 11.93 0.000   F_0.05,4,15=3.0556
Interaction 8 3.8000 0.47500 0.65 0.728 F_0.05,8,15=2.6408
Error 15 11.0000 0.73333
Total 29 58.6667

From the ANOVA table we observed that p-value corresponding interaction effect=0.728>0.05 hence we conclude that the interaction effect is insignificant. Now p-vlaue of Car=0.000<0.05 hence car types are significantly different from each other. Again, p-value of Wax Type=0.012<0.05, hence three waxes are not equally effective.