Question

You are a field engineer working for Far North Arctic Insulates Inc. Your company has come up with a new insulation material to be used under road beds to keep the permafrost from warming during the summer months. Since this material is quite costly, you want to be able to use the least amount of material (i.e., smallest thickness possible). You have collected the following temperature data (in degrees-Fahrenheit) from thermistor readings at a depth of seven feet at eight different test locations: three on the University of Alaska Fairbanks campus (UAF1, UAF2, UAF3); two from sites on Farmers Loop (FL1, FL2); and three from locations on the Steese Highway (ST1, ST2, ST3). Use α = 0.05 for all procedures where appropriate.

(a) Present appropriate data summaries of the temperature readings (e.g., box plots, histograms, marginal plots, dot diagrams, etc.).

(b) Assess the normality assumption for the temperature readings.

(c) Perform the hypothesis testing procedure to determine whether there is a statistically significant difference in ground temperature between insulation thicknesses. Report the appropriate results table. Show calculations for sum of squares (SS), mean squares (MS), and test statistic. Note: everything else can be done using statistical software of your choosing except here show work for SS, MS and test statistic calculations; however, feel free to check your work with software.

(d) Determine the P-value associated with the test conducted in Part (a).

(e) Which specific thicknesses are different? Report the mean values and confidence intervals (as plots or tables).

(f) Analyze and interpret the residuals from this experiment (i.e., model checking).

(g) State the practical conclusions that can be drawn from this experiment. Include a memo to your “boss” that indicates what you have found and the appropriate course of action.

Insulation thickness (in) Site ID

UAF1 UAF2 UAF3 FL1 FL2 ST1 ST2 ST3
3.00    17.3 17.1 17.5 14.2 14.5 16.5 18.0 18.2
2.00 18.1 19.6 22.7 17.1 16.9 22.2 18.1 21.3
1.00 23.2 24.2 22.9 16.7 18.1 23.9 24.1 25.6
0.75 24 24.5 23.9 19.4   19.6 24.5 24.6 25.0
0.50 29.1 28.8 34.3 32.6 33.0 27.3 29.4 30.8
0.25 38.6 30.2 35.7 36.8 32.5 29.7 31.9 34.2

Answer 1