4.88. Cost of modifying a naval air base. A naval base
is considering modifying or adding to its ﬂeet of 48 standard aircraft. The ﬁnal decision regarding the type and number of aircraft to be added depends on a comparison of cost versus effectiveness of the modiﬁed ﬂeet. Consequently, the naval base would like to model the projected percentage increase y in ﬂeet effectiveness by the end of the decade as a function of the cost x of modifying the ﬂeet. A ﬁrst proposal is the quadratic model
E(y) = β0 + β1x + β2×2
The data provided in the table were collected on 10 naval bases of similar size that recently expanded their ﬂeets.
where y = Emotional distress
x1 = Experience (years)
x2 = 1 if exposed to chemical ﬁre, 0 if not
(a) What hypothesis would you test to determine whether the rate of increase of emotional dis- tress with experience is different for the two groups of ﬁreﬁghters?
(b) What hypothesis would you test to determine whether there are differences in mean emo- tional distress levels that are attributable to exposure group?
(c) Data for a sample of 200 ﬁreﬁghters were used to ﬁt the complete model as well as the reduced
1 model, E(y) = β0 + β1×1 + β2×2. The results are SSER = 795.23 and SSEC = 783.90. Is
there sufﬁcient evidence to support the claim
that the mean emotional distress levels differ for the two groups of ﬁreﬁghters? Use α = .05.