Use calculator or Excel to solve the following problems.DO NOT USE MINITAB (except e). Do NOT use Excel built-in functionsor solvers (except t.inv() and f.inv() to obtain critical t and fvalues).

The tensile strength of Portland cement is being studied. Fourdifferent mixing techniques can be used economically. A completelyrandomized experiment was conducted and the following data werecollected:

Technique	Tensile Strength	Tensile Strength	Tensile Strength	Tensile Strength
1	3129	3000	2865	2890
2	3200	3300	2975	3150
3	2800	290	2985	3050
4	2600	2700	2600	2765

a) Test the hypothesis that mixing techniques affect thestrength of the cement (? = 0.05).

b) Use the Fisher LSD method with ? = 0.05 to make comparisonsbetween pairs of means.

c) Repeat part (b) using Tukey’s test. Do you get the sameconclusions as part (b)? If not, explain why.

d) Find a 95 percent confidence interval on the mean tensilestrength of the Portland cement produced by each of the four mixingtechniques. Also find a 95 percent confidence interval on thedifference in means for techniques a and c.

e) Construct a normal probability plot of the residuals and aplot of residuals vs. predicted values (using Minitab). Whatconclusion would you draw from each plot?

f) Suppose Technique d is the current mixing technique. We wouldlike to compare it with the average effect of the new techniques(Techniques a, b and c). Also, we are interested in whetherTechnique b is significantly different from the average effect ofthe two other new techniques (Techniques a and c). Construct therequired contrasts to test these and apply Scheffe’s method to makeconclusions. Set ? = 0.05