Only use R for both problems and send the codes
Problem 1
Consider an experiment taste-testing four types of chocolate chip cookies: 1 (brand A, chewy,expensive), 2
(brand B, crispy, expensive), 3 (brand C, chewy, inexpensive), 4 (brand D, crispy, inexpensive). We will use
ten different raters randomly assigned to each type (40 total raters). Answer the following questions:
a. Design contrasts to compare chewy with crispy, and expensive with inexpensive.
b. Are your contrasts in part a) orthogonal? Why or why not?
Problem
2
A consumer testing agency obtains four cars from each of six makes: Problem 4.1 Ford, Chevrolet, Nissan,
Lincoln, Cadillac, and Mercedes. Makes 3 and 6 are imported while the others are domestic; makes 4, 5,
and 6 are expensive, while 1, 2, and 3 are less expensive; 1 and 4 are Ford products, while 2 and 5 are GM
products. We wish to compare the six makes on their oil use per 100,000 miles driven.
where the car markers are coded from 1 to 6 corresponding to Ford, Chevrolet, Nissan, Lincoln, Cadillac, and
Mercedes, respectively. Data are recorded in the response variable.
a. Compute the Analysis of Variance table for this experiment. What would you conclude?
b. There are many meaningful contrasts that can be construced. Consider two of them below. Design
the contrasts to answer the following research questions and obtain the corresponding 95% confidence
interval for two-sided alternatives. Report the meaning of confidence interval for each contrast.
1. Design a contrast to compare the oil use in imported cars with that in exported cars.
2. Design a contrast to compare the oil use in cheap cars with that in expensive cars.
(please note that you need to change the format from .docx to .csv in order to be able to open the data, i was not able to upload the csv file)
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