Question

5. 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 a. Write the Null and Alternative hypothesis to test whether there is a difference in dry time between the samples of each paint? b. What statistic would you use to analyze this? c. At a 0.01 level of significance, what would be your decision rule? d. From your analysis, is there a difference between drying times? e. 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

a) Null and Alternative hypothesis are-

H_0: No difference in dry times of the different paints

H₁:There is a difference in dry times of the different paints

b) I have used F test to analysis this, using ANOVA model

c) The ANOVA Table is-

SUMMARY
Groups	Count	Sum	Average	Variance
paint1	7	849	121.2857143	38.23809524
paint2	7	871	124.4285714	25.95238095
paint3	7	859	122.7142857	25.57142857
paint4	7	864	123.4285714	60.61904762
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	36.67857143	3	12.22619048	0.325205826	0.807100713	3.00878657
Within Groups	902.2857143	24	37.5952381
Total	938.9642857	27

Since, P-value=0.807>0.01, then at alpha=0.01 we do not reject the null hypothesis(Because the value of test statistic F falls in acceptance region)

d)Since we have accepted the null hypothesis, then there is no difference in dry times of different paints.