Hello, dear friend, you can consult us at any time if you have any questions, add WeChat: daixieit

Midterm (take-home) (30 pts)

STA 404

Due: 3/14 by 4:00 PM

A team of researchers investigating blood flow to the brain performed a study using laboratory mice. To simulate cardiovascular disease in humans, the bloody supply to each mouse’s brain was restricted by artificially blocking the cerebral artery. Each mouse was given one of three treatments. At a predetermined time, each mouse’s brain was dissected to determine the amount of brain tissue that died (known as infarction volume) from lack of blood flow. The data are contained in the file mouse_brain24.txt. While one of the treatments represents a control group, the study protocol called for the statisticians to be blinded; hence the data set only refers to the treatments as 1, 2, or 3.

a) Import the data in Minitab. Verify that you have correctly done so by presenting the grand sample mean as 64.6431. (1)

b) What are the values of  and  for this experiment? (2)

c) Produce a set of group-specific boxplots of the response variable. Comment on the observed sample means. (3)

d) Fit the one-way ANOVA model and provide the ANOVA table. (2)

e) Carry out the ANOVA F-test, stating the hypotheses, test statistic, p-value, and conclusion in context. (4)

f) We now wish to consider individual tests of the following form:

Carry out all pairwise tests using the Tukey correction for multiple comparisons. Present a table of output containing the simultaneous confidence intervals and adjusted p-values. Highlight any comparisons that indicate a significant group difference. (4)

g) Present a plot of residuals vs fitted values and discuss whether the assumption of constant variance seems justified. (3)

h) Execute Levene’s test. Present the hypotheses, p-value, and conclusion. (3)

i) Execute the Ryan-Joiner test on the model residuals. Present the hypotheses, p-value, and conclusion. (3)

j) Carry out the Kruskal-Wallis test using the mouse data. State the hypotheses, p-value, and conclusion in context. (3)

k) Give a recommendation as to which treatment(s) is/are preferred. Provide justification. (2)