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5. Four different paints are advertised to have the same drying times. To verify the manufacturer’s...

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5. Four different paints are advertised to have the same dryingtimes. To verify the manufacturer’s claim, seven samples weretested for each of the paints. The time in minutes until the paintwas dry enough for a second coat to be applied was recorded. Beloware the results which may be imported into MSExcel for analysis:(Assume the populations are normally distributed, the populationsare independent and the population variances are equal) Paint 1Paint 2 Paint 3 Paint 4 120 120 117 128 112 130 122 131 121 121 123131 118 126 115 129 118 126 123 127 121 114 126 126 118 117 126 137a. Write the Null and Alternative hypothesis to test whether thereis 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 ofsignificance, what would be your decision rule? d. From youranalysis, is there a difference between drying times? e. If therewas a difference in dry times how would you determine which painthas the different drying time? (i.e. what formula would you use andwhat is your decision criteria?) (this is not asking for acalculation)

Answer & Explanation Solved by verified expert
4.0 Ratings (771 Votes)

a) Null and Alternative hypothesis are-

H0: 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.
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