In Exercise 8.16 on page 506, we discuss a study investigating the effect of ink color on performance in an anagram test. Three different colors were used with a total of 71 participants. The red group contained 19 participants and they correctly solved an average of 4.4 anagrams. The 27 participants in the green group correctly solved an average of 5.7 anagrams and the 25 participants in the black group correctly solved an average of 5.9 anagrams. From the analysis of variance in Exercise 8.16, we see that there is a significant difference between the groups and that the mean square error from the ANOVA table is 0.84.
(a) Find and interpret a 95% confidence interval for the mean number of anagrams we expect people to solve when the ink is red.
(b) Find and interpret a 95% confidence interval for the difference in mean number of anagrams we expect people to solve between when the ink is green and when it is red.
(c) Test whether there is a significant difference in means between when the ink is red and when it is black.

Exercise 8.16

In a recent study, 2006 randomly selected US adults (age 18 or older) were asked to give the number of people in the last six months ‘‘with whom you discussed matters that are important to you.” The average number of close confidants was 2.2, with a standard deviation of 1.4.