Fall 2005 Stat
514 Test 2 Take Home problems
1. To compare the performance of students in three large sections of
an introductory college course, six students were randomly sampled from each section, and
their scores from a common exam were recorded. The scores were 67, 72, 75, 89, 94,
and 45 in section 1; 73, 79, 91, 97, 88, and 93 in section 2; and 69, 24, 71, 76, 66, and
85 in the section 3. Do both a parametric and a nonparametric test of the null
hypothesis of no difference in exam means in the three sections, and also use a
permutation HSD method to test all pairwise differences between sections.
2. Students in a southern California elementary school were asked to
pick their favorite theme park from among Disneyland, Legoland, and Six Flags Marine
World. Of the three boys interviewed, 2 picked Legoland and 1 picked Six Flags
Marine World as their favorite. Three girls were interviewed and 2 of them picked
Six Flags Marine World while one of them picked Disneyland as their favorite. Do boys and
girls have different theme park preferences? Conduct a homogeneity of proportions
test by enumerating the permutation distribution for the chi-squared statistic for these
data, and make your conclusion based on the permutation p value.
3. We have often used general scores to analyze data instead of just
ranks. The two types that we have used the most are Van der Waerden scores and
Savage scores. When conducting the Wilcoxon signed-rank test, one of these two
scores can be directly applied, while the other is not as easily applied, when using the
instructions given in section 4.3.2 of the text. Which type of score can be easily
applied, which type is not as easy to directly apply? Why is one of them not as easy
to apply?