Question

3. Four different paints are advertised to have the same drying times. To verify the manufacturer’s claim, 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 which may be imported into MSExcel for analysis: (Assume the populations are normally distributed, the populations are independent and the population variances are equal)

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

1. Write the Null and Alternative hypothesis to test whether there is a difference in dry time between the samples of each paint?

2. What statistic would you use to analyze this?

3. At a 0.01 level of significance, what would be your decision rule?

4. From your analysis, is there a difference between drying times?

5. If there was a difference in dry times how would you determine which paint has the different drying time? (i.e. what formula would you use and what is your decision criteria?) (this is not asking for a calculation)

Answer 1

Solution

We will perform One Way Anova to find the solution using Excel

So the output for One Way Anova is obtained using excel are given below

Anova: Single Factor
SUMMARY
Groups	Count	Sum	Average	Variance
paint 1	7.0000	828.0000	118.2857	9.5714
paint 2	7.0000	854.0000	122.0000	31.6667
paint 3	7.0000	852.0000	121.7143	17.9048
paint 4	7.0000	909.0000	129.8571	13.4762
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	503.2500	3.0000	167.7500	9.2400	0.0003	4.7181
Within Groups	435.7143	24.0000	18.1548
Total	938.9643	27.0000

Write the Null and Alternative hypothesis to test whether there is a difference in dry time between the samples of each paint?

What statistic would you use to analyze this?

We will use F -statistic

F-statistic = 9.2400

At a 0.01 level of significance, what would be your decision rule

Since F-statistic = 9.2400 > F critical = 4.7181 so we reject the null hypothesis, at 0.01 level of significance.

From your analysis, is there a difference between drying times?

Since we are rejecting the null hypothesis so we have enough evidence to conclude that there is a difference between drying times.

If there was a difference in dry times how would you determine which paint has the different drying time?

F-statistic = 9.2400 > F critical = 4.7181