3. A study conducted at Delphi Energy & Engine Management Systems considered the effect of blow-off pressure during the manufacture of spark plugs on the spark plug resistance. The resistance measurements of 150 spark plugs manufactured at each of three different blow-off pressures (10, 12, and 15 psi) yield the following summary statistics: X1 = 5.365, X2 = 5.415, X3 = 5.883, S21

= 2.241, S22

= 1.438, and S23

= 1.065. Is there evidence that the blow-off pressure affects the average spark plug resistance?

(a) State the relevant null and alternative hypotheses for answering this question, and use hand calculations to conduct the ANOVA F test at level of significance 0.05. State any assumptions needed for the validity of this test procedure.

(b) Use the Bonferroni multiple comparisons method, with pair wise two-sample T tests using the equalvariance assumption, to identify the groups whose population means differ significantly at experimentwise level of significance α = 0.05. Summarize your results by arranging the means in increasing order and underlining the ones that do not differ significantly.