Question: Refer to the data for problem. Select the two additives with the largest average difference in waste and answer the following. (Use the least-significant difference test method for this problem, subtracting smaller from larger even if you feel that it is not appropriate to do so.)

a. Find the size of the average difference for this pair.

b. Find the standard error of this average difference.

c. How many degrees of freedom does this standard error have?
d. Find the two-sided 90% confidence interval for the mean difference.

Problem: Three companies are trying to sell you their additives to reduce waste in a chemical manufacturing process. You are not sure their products are appropriate because your process is different from the industry standard (it is a proprietary trade secret). You have arranged to get a small supply of each additive, provided free, for testing purposes. Table shows the summaries of the waste measurements when each additive was used, all else kept equal.

a. Which additive appears to leave the highest amount of waste? Which appears to leave the lowest?

b. Find the total sample size, n, the grand average, X, and the number of samples, k.

c. Find the between-sample variability and its degrees of freedom.

d. Find the within-sample variability and its degrees of freedom.

e. Based on the average difference, the standard error, the degrees of freedom, and the critical t value, do these two additives appear to be significantly different at the 10% test level?

f. Can you conclude that the two additives are really significantly different at the 10% level? Why or why not? (Be careful. You may wish to consider the result of the F test from the preceding problem.)