Question

To be done on Anova (or not)

A5 An experiment was run to determine whiter four specific firing temperature affect the density of a certain type of brick. The experiment led to the following data. Does the firing temperature affect the density of the bricks? Temp. 100 125 150 175 21.8 21.7 20.9 21.6 Density 21.9 21.7 21.4 21.5 20.8 21.1 20.9 21.5 21.6 21.4 21.2 21.4 21.7 21.3 20.7 21.6

1. State the hypothesis that we are testing in this problem.
2. Set up the null and alternative.
3. Comment on the degree of freedom values for each source of variation. How do you calculate them?
4. Do we reject the hypothesis that we are testing? Why or why not?
5. If you reject, can you tell which level(s) is probably the one(s) that has the different mean? (Hint: use the box plots from part 1a
6. Use the histogram of residuals to comment on the normality of error term
7. If you are suspicious of only one level, repeat the ANOVA without that level and see if you fail to reject the null in the test.

Answer 1

(a) The hypothesis being tested is:

H0: µ1 = µ2 = µ3 = µ4

Ha: At least one means is not equal

	Mean	n	Std. Dev
	21.74	5	0.114	100 F
	21.50	4	0.141	125 F
	21.72	5	0.164	150 F
	21.70	4	0.216	175 F
	21.67	18	0.174	Total
ANOVA table
Source	SS	df	MS	F	p-value
Treatment	0.156	3	0.0520	2.02	.1569
Error	0.360	14	0.0257
Total	0.516	17

Since the p-value (0.1569) is greater than the significance level (0.05), we cannot reject the null hypothesis.

Therefore, we cannot conclude that the firing temperature affect the density of the bricks.

(b) No, because there is no significant difference.

(c) The assumptions are met.