2. A tea company wants to assess the amount of caffeine in their black, green,

oolong, and white teas. They take a random sample of leaves from 10 batches of each type

of tea. They make one, 8-oz cup of tea from each sample (40 cups altogether), brewing each

for 2 minutes. They then measure the amount of caffeine (in mg) in each. You may assume

that the caffeine measurements are independent. The data are available in the file tea.txt.

a. Produce boxplots of the caffeine measurements for the four types of tea. Be

sure to label the axes appropriately.

b. Write down the factor effects version of an ANOVA model for these data.

Be sure to define your variables and to state all assumptions.

c. Fit the model in (b) and provide the table of parameter estimates, standard

errors, etc.

d. What is the estimated mean amount of caffeine per 8 oz of each type of tea?

e. Are the caffeine measurements approximately normally distributed? Justify

your answer.

f. Is the standard deviation of the caffeine measurements approximately the

same for each type of tea? Justify your answer.

g. The company is interested in whether the amount of caffeine, on average,

varies among the different types of tea.

i. Specify the null and alternative hypotheses in terms of the parameters of the

model in (b).

ii. Choose an appropriate test and specify the value of the test statistic.

iii. Specify the p-value.

iv. Using a significance level of = 0.01, state your conclusions in the language

of the problem.