480 Chapter 10:Analysis of Variance
(a) Test the hypothesis of no age and gender interaction.
(b) Test the hypothesis that gender does not affect the blood concentration.
(c) Test the hypothesis that age does not affect blood concentration.
27.Suppose, in Problem 23, that there has been some controversy about the assump-
tion of no interaction between gasoline and additive used. To allow for the
possibility of an interaction effect between gasoline and additive, it was decided to
run 36 motors—4ineach grouping. The following data resulted.Additive
Gasoline 1 2 3
1 126.2 130.4 127
124.8 131.6 126.6
125.3 132.5 129.4
127.0 128.6 130.1
2 127.2 142.1 129.5
126.6 132.6 142.6
125.8 128.5 140.5
128.4 131.2 138.7
3 127.1 132.3 125.2
128.3 134.1 123.3
125.1 130.6 122.6
124.9 133.0 120.9(a) Do the data indicate an interaction effect?
(b) Do the gasolines appear to give equal results?
(c) Test whether or not there is an additive effect or whether all additives work
equally well.
(d) What conclusions can you draw?
28.An experiment has been devised to test the hypothesis that an elderly person’s
memory retention can be improved by a set of “oxygen treatments.” A group of
scientists administered these treatments to men and women. The men and women
were each randomly divided into 4 groups of 5 each, and the people in theith
group were given treatments over an (i−1) week interval,i=1, 2, 3, 4. (The
2 groups not given any treatments served as “controls.”) The treatments were set
up in such a manner that all individuals thought they were receiving the oxygen
treatments for the total 3 weeks. After treatment ended, a memory retention
test was administered. The results (with higher scores indicating higher memory
retentions) are shown in the table.
(a) Test whether or not there is an interaction effect.
(b) Test the hypothesis that the length of treatment does not affect memory
retention.