In a statement to a Senate Public Works Committee, a senior executive of Texaco, Inc. cited a study on the effectiveness of auto filters on reducing noise. Because of concerns about performance, two types of filters were studied, a standard silencer and a new device developed by the Associated Octel Company. Here are the box plots from the data on noise reduction (in decibels) of the two filters. Type 1 = standard; Type 2 = Octel.

a) What are the null and alternative hypotheses?
b) What do you conclude from the ANOVA table?
c) Do the assumptions for the test seem to be reasonable?
d) Perform a two-sample pooled t-test of the difference. What P-value do you get? Show that the square of the f-statistic is the same (to rounding error) as the F-ratio.

2 654321098765 888888877777 (slagoap) esiON Sum of Mean Source DF Squares Square -Ratio P-Value Type 1 6.3 6 0.7673 0.3874 Error 33 27147 8.23 Total 34 722.78 Means and Std Deviations n Mean StdDev Standard 18 81.5556 3.2166 Octel 17 80.7059 2.43708