MATH 208 Assignment 4


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MATH 208 Assignment 4
The assignment contains one questions, each with 5 parts (a)-(e) worth 10 points, for a total of 50 points.
Your answers must be submitted in the form of a PDF and include both the answers to the question, along
with your R code and output used to generate your answers.
Question 1
The data for this question come from a high performance ceramics experiment done at NIST. The purpose of
the experiment was to characterize the effect of five machining factors on the mean strength of the resulting
ceramic. The five factors were: Table Speed, Down Feed Rate, Wheel Grit, Direction, and Batch.
Each factor had two levels. The Mean Speed was measured for each of the 2
5 = 32 possible combinations of
factor levels.
You can read in the data from the file attached to the Assignment on myCourses by using
Remember that the ceramic.txt file must be in your current working directory, or you need to specify an
alternate path.
(a) What class of object is ceramic_data?
(b) Using the ceramic_data object, compute the median Mean_Strength by Batch, i.e. write a line of
code that produces a vector that computes the mean of all observations in each batch, respectively.
What is the difference in mean by Batch?
(c) Compute the overall standard devation of the Mean_Strength values across all 32 observations.
Hint: remember that this type of object is stored internally as an generic vector.
(d) Using the ceramic_data object, compute the average Mean_Strength for each of the four groups
defined by the cross-classification of Table_Speed and Direction. Hint: the most succinct way to do
this would return a 2×2 table with Table_Speed levels in the rows and Direction levels in the columns.
(e) Compute the difference in means between the Longitudinal and Transverse levels of Direction for each
level of Slow and Fast separately. Hint: Use part (d) and the apply function.

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