Question

Particulate matter is a serious form of air pollution often arising from industrial production. One way to reduce the pollution is to put a​ filter, or​ scrubber, at the end of the smokestack to trap the particulates. An experiment to determine which smokestake scrubber design is best was run by placing four scrubbers of different designs on an industrial stack in random order. Each scrubber was tested five times. For each​ run, the same material was​ produced, and the particulate emissions coming out of the scrubber were measured​ (in parts per​ billion).

Click on the icon to view the partially completed analysis of variance table of the data.

Source Sum of Squares Degrees of Freedom Mean Square F-ratio

Treatment 80.1

Residual/Error 36.9

Total 117

​a) Calculate the mean square of the treatments and the mean square of the error.

Compute the mean square of the treatments.

MSt = _ ?

(Round to three decimal places as​ needed.)

Compute the mean square error.

MSe = _ ?

​(Round to three decimal places as​ needed.)

b) Form the​ F-statistic by dividing the two mean squares.

F = _ ?

​(Round to two decimal places as​ needed.)

​c) The​ P-value of this​ F-statistic is 0.00002962. What does this say about the null hypothesis of equal​ means? Use a=0.01.

(Reject/ Do not reject) the null hypothesis. There is (sufficient/ is not sufficient) evidence to infer that the mean particulate emissions of the different designs are not equal.

​f) Provide an estimate for the standard deviation in the amount of particulate emitted by each of the filters.

The pooled standard deviation is equal to _ ?

​(Round to two decimal places as​ needed.)

Answer 1

(a) MSt = 26.7

MSe = 2.306

(b) F = 11.58

(c) Reject the null hypothesis. There is sufficient evidence to infer that the mean particulate emissions of the different designs are not equal.

(f) 1.52

Source	SS	df	MS	F	p-value
Treatment	80.1	3	26.7	11.58	0.0002772
Error	36.9	16	2.306
Total	117	19