Question

10. Four different paints are advertised to have the same drying times. Use the Kruskal Wallis Test – Analysis of Variance by Ranks, to verify the manufacturer’s claim.  Remember that seven samples were tested for each of the paints. The time in minutes until the paint was dry enough for a second coat to be applied was recorded.  Below are the results.    

Paint 1	Rank	Paint 2	Rank	Paint 3	Rank	Paint 4	Rank
114		112		126		115
117		118		127		117
120		118		128		122
121		118		129		123
126		120		131		123
126		121		131		126
130		121		137		126

H₀: the population distributions of drying times are the same for the four samples

H₁: the population distributions of drying times are not all the same for the four samples

1. State your test statistic:

2. State your decision rule: (α = 0.05)

3. Show your calculation:

4. What is your conclusion?

Answer 1

H₀: the population distributions of drying times are the same for the four samples

H₁: the population distributions of drying times are not all the same for the four samples

Paint 1	Rank	Paint 2	Rank	Paint 3	Rank	Paint 4	Rank
114	2	112	1	126	19	115	3
117	4.5	118	7	127	22	117	4.5
120	9.5	118	7	128	23	122	14
121	12	118	7	129	24	123	15.5
126	19	120	9.5	131	26.5	123	15.5
126	19	121	12	131	26.5	126	19
130	25	121	12	137	28	126	19
	T: 91		T: 55.5		T: 169		T: 90.5
	n: 7		n: 7		n: 7		n: 7

Test statistic = H = (12/(N(N+1)) * ($\sum$T²/n) - 3(N+1)

N = total number of observations = 28

H = 0.015 * 6873.214 - 87

H = 14.5746

The p-value is .00222. Since the p-value is less than α we reject null hypothesis hence we conclude that the population distributions of drying times are not all the same for the four samples