Question

	Porosity%	Mean diameter(mm)
A	18	12
B	18.3	9.7
C	16.3	7.3
D	6.9	5.3
E	17.1	10.9
F	20.4	16.8

1.

a. Construct an ANOVA table to assess the relationship between porosity and mean pore diameter

b. Indicate your hypotheses

c. Make sure you can do the computations by hand. Show your work (you can doublecheck using software)

d. Compute an F test statistic. Using a Type I error rate of 10% (as opposed to the more traditional 5%), conclude and interpret.

e. Compute the P-value. Interpret it.

f. Compute the coefficient of determination and interpret it.

Answer 1

(a)

Source	SS	df	MS	F	p-value
Regression	72.0410	1	72.0410	7.11	.0561
Residual	40.5523	4	10.1381
Total	112.5933	5

(b) The hypothesis being tested is:

H₀: µ₁ = µ₂

H_a: Not all means are not equal

(c)

	r²	0.640
	r	0.800
	Std. Error	3.184
	n	6
	k	1
	Dep. Var.	Porosity%
ANOVA table
Source	SS	df	MS	F	p-value
Regression	72.0410	1	72.0410	7.11	.0561
Residual	40.5523	4	10.1381
Total	112.5933	5
Regression output					confidence interval
variables	coefficients	std. error	t (df=4)	p-value	95% lower	95% upper
Intercept	6.3518
Mean diameter(mm)	0.9498	0.3563	2.666	.0561	-0.0395	1.9391

(d) The F test statistic is 7.11.

(e) The p-value is 0.0561.

(f) 0.640.