Question

Power plants can emit levels of pollution that can lower air quality. For this reason, it is important to monitor the levels of pollution they produce. Investigators measured dust emissions, in milligrams per cubic meter, at four power plants. Thirty measurements were taken for each plant. The sample means and standard deviations are presented in the table. Can you conclude there are differences among the mean emission levels at significance level 0.05?

Plant	Mean	Standard Deviation	Sample Size
A	211.50	24.85	30
B	214.00	35.26	30
C	211.75	33.53	30
D	236.08	23.09	30

Answer 1

from above data:

Group	ni	x̅i	S2i	ni*(Xi-Xgrand)2	(ni-1)*S2i
A	30	211.5	617.523	1400.492	17908.15
B	30	214	1243.268	563.117	36054.76
C	30	211.75	1124.261	1299.879	32603.57
D	30	236.08	533.148	9449.213	15461.29
	grand mean=	218.3325		12712.700	102027.77
				SSTr	SSE

Source	SS	df	MS	F	Fcrit
between	12712.70	3.000	4237.5668	4.82	2.683
within	102027.77	116.000	879.5498
total	114740.47	119.0000

as test statistic Falls above critical value we reject null hypothesis

therefore we have sufficient evidenec to conclude that there are differences among the mean emission levels at significance level 0.05 .