16. Auto noise filters 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 boxplots from the data on noise reduction (in decibels) of the two filters. Type 1 = standard; Type 2 = Octel.

ANOVA Table Source DF Sum of Squares Mean Square F-Ratio P-Value Type 1 6.31 6.31 0.7673 0.3874 Error 33 271.47 8.22 Total 34 2.77 Means and Std Deviations Level n Mean StdDev Standard 18 81.5556 3.2166 Octel 17 80.7059 2.43708

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 t-statistic is the same (to rounding error) as the F-ratio.

Noise (decibels) H 995 1 2