Question

Four catalysts that may affect the concentration of one component in a three-component liquid mixture are being investigated. The following concentrations are obtained from a completely randomized design.

Catalyst
1	2	3	4
58.2	56.3	50.1	52
57.7	54.5	54.2	49.9
58.4	57.0	55.4	50
55.8	55.3		51.7
54.9

(d) Write an appropriate statistical model with fixed effects.

(e) State clearly your null and alternative hypothesis. Perform ANOVA. What is your conclusion? You should be able to solve this question by hand with computational formula.

(f) Obtain the appropriate residual plots and comment on the plots.

Answer 1

(d)

Regression Equation

1

=

57.000 + 0.0 2_1 - 1.22 2_2 - 3.77 2_3 - 6.10 2_4

(e)

Null hypothesis	All means are equal
Alternative hypothesis	Not all means are equal
Significance level	α = 0.05

Equal variances were assumed for the analysis.

Factor Information

Factor	Levels	Values
2	4	1, 2, 3, 4

Analysis of Variance

Source	DF	Adj SS	Adj MS	F-Value	P-Value
2	3	94.38	31.461	11.63	0.001
Error	12	32.47	2.706
Total	15	126.86

Since the p-value (0.001) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we can conclude that not all means are equal.

(f) The plot is:

The residuals are normally distributed.