Question

3. 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

Solution-

firstly data is arranged in ascending order. then ranks are assigned. then for ties ranks are adjusted.(in calculations part- c)

Data Assign with ranks-

Paint 1	Rank	Rank (Adjusted for ties)	Paint 2	Rank	Rank (Adjusted for ties)	Paint 3	Rank	Rank (Adjusted for ties)	Paint 4	Rank	Rank (Adjusted for ties)
114	2	2	112	1	1	126	19	19	115	3	3
117	4	4.5	118	6	7	127	22	22	117	5	4.5
120	9	9.5	118	7	7	128	23	23	122	14	14
121	11	12	118	8	7	129	24	24	123	15	15.5
126	17	19	120	10	9.5	131	26	26.5	123	16	15.5
126	18	19	121	12	12	131	27	26.5	126	20	19
130	25	25	121	13	12	137	28	28	126	21	19

a) Test Statistics-

H= 14.575 or =14.575

b) Decision Rule(critical value and p-value approach)-

c) Calculations-

d) Conclusion-

Null hypothesis Ho is rejected. so we have Not enough evidence to support the manufacturer's claim that Four different paints are advertised to have the same drying times.

in other words-

H1 is accepted. so, the population distributions of drying times are not all the same for the four samples.