Question

Use Minitab to solve the following:

1. Zeolites are aluminum and silicon crystals that are used as sieves and catalysts in many industries – especially petroleum refining. The relative yields (in percent) of the 16 most recent batches of zeolite produced by a particular manufacturer are as follows (in order of production):

39.5     33.3     36.2     33.0     40.4     31.1     40.1     44.4     35.7     33.4

42.6     34.5     35.7     29.5     35.3     37.8

a) Is it reasonable to assume that the population associated with the sample is normally distributed? Give a reason for your answer.

b) Obtain a point estimate for the population mean yield, m, and the population standard deviation.

c) Construct and interpret a 95% confidence interval for the mean yield.

d) Construct a 95% prediction interval estimate for the yield of the next zeolite batch.

e) For planning purpose, management needs a range of values in which they are 95% confident will encompass at least 99% of all batch yields. Construct an interval that will meet their needs.

f) Compare the results in parts c), d), and e) and explain the differences.

g) Construct a 95% confidence interval for the population standard deviation.

Answer 1

a) We provide a PP plot and observe that the points lie mostly on the central line and hence normality seems justified.

b)The points estimate of population mean is sample mean and that of population sd is sample sd. We calculate sample mean=36.41 and sample sd=4.126.

c) The CI based on the t distribution is  (34.21, 38.61).

Thus in the long run the above interval is expected to contain the true value in 95% cases.

d) The prediction interval is ( 27.34498,45.47502).

g) The chi square distribution based 95% CI for population sd is ( (3.05, 6.39)