The study referred to in Exercise 10 in Sec. 11.6 actually included another factor in addition to size of vehicle. There were two different filters, a standard filter and a newly developed filter. Table 11.19 has data only from the standard filter. The corresponding data for the new filter are in Table 11.31.

a. Construct the ANOVA table for the two-way layout that includes the data from both Tables 11.19 and 11.31.
b. Compute the p-value for testing the null hypothesis that there is no interaction.
c. Compute the p-value for testing the null hypothesis that the vehicles of all three sizes produce the same level of noise on average.
d. Compute the p-value for testing the null hypothesis that both filters result in the same level of noise on average.

Vehicle size Small Medium Large Noise values 820, 820, 820, 825, 825, 825 820, 820, 825, 815, 825, 825 775, 775, 775, 770, 760, 765