STAT question

STAT 3300 Homework #9 Due Thursday, 05/28/2020

Note: Answer these questions on a separate piece of paper. In the top right corner, include your name, SMU ID, and course number. Please include a title for the assignment so that it is clear to the graders. If you miss class the day the assignment is turned in, submit this before class in order to receive credit.

Question 1 (35 points total, 7 points each) According to William Butler Yeats, “She is the Gaelic muse, for she gives inspiration to those she persecutes. The Gaelic poets die young, for she is restless, and will not let them remain long on earth.” One study designed to investigate this issue examined the age at death for writers from different cultures and genders. Three categories of writers examined were novelists, poets, and nonfiction writers. Most of the writers are from the United States, but Canadian and Mexican writers are also included. The data are given in “ex12-46poets.csv”. Use R to answer the following:

a) Examine the assumptions necessary for ANOVA. Summarize your findings.

b) Run the ANOVA and report the results. Include the null and alternative hypotheses, the test statitsic, the p-value, and a conclusion in the context of the problem.

c) Use a contrast to compare the poets with the two other types of writers. Use a one-sided alternative based on the quote from Yeats (poets die at a younger age). Note that the levels of “Type” are non-fiction, novels, and poems; non-fiction is group 1, novels is group 2, and poems is group 3.

d) Use another contrast to compare the novelists with the non-fiction writers.

e) Construct a boxplot for the three groups of writers. Use the Bonferroni procedure to compare the three means (α = 0.05). The data are in “ex12-46poets.csv”.

Question 2 (32 points total, 8 points each) Each of the following tables gives means for a two-way ANOVA. Make a plot of the means with the levels of Factor A on the x axis. State whether or not there is an interaction, and if there is, describe it.

1

Question 3 (33 points total) Not only does speaking two languages have many practical benefits in a globalized world, but there is also growing evidence that it appears to help with brain functioning as we age. In one study, 80 participants were divided equally among 4 groups: younger adult bilinguals, older adult bilinguals, younger adult monolinguals, and older adult monolinguals. Each participant was asked to complete a series of color-shape task-switching tests. For our analysis, we’ll focus on the total reaction time (in microseconds) for these experiments; the shorter the reaction time, the better. The data are in “EX13-22BILING.csv”.

a) (9 points) Make a table giving the sample size, mean, and standard deviation for each group. Is it reasonable to pool the variances?

b) (9 points) If bilingualism helps with brain functioning as we age, explain why we’d expect to find an interaction between age and lingualism. Also create an interaction plot that shows the type of pattern we’d expect.

c) (15 points) Analyze the data using an ANOVA. Report the test statistics, degrees of freedom, and p-values (α = 0.10). Write a short paragraph summarizing your findings.

2