5.4 26 Problem 2: In a large construction project, two different brands of latex (water-based) paint are being considere

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5 4 26 Problem 2 In A Large Construction Project Two Different Brands Of Latex Water Based Paint Are Being Considere 1 (66.52 KiB) Viewed 22 times

5.4 26 Problem 2: In a large construction project, two different brands of latex (water-based) paint are being considered to be used. The choice between the brands, is based on a key factor; that is the time it takes the paint to dry. Engineers sampled 30 specimens of each brand and measured the drying times in hours) of each specimen. The data collected are given in Table below. | Specimen Brand A Brand B Specimen Brand A Brand B 1 3.5 4.7 16 5.2 6.2 2 2.7 3.9 17 4.0 5.1 3 3.9 4.5 18 4 4.2 5.5 19 3.4 4.8 5 4.6 4.0 20 3.3 4.9 6 2.7 5.3 21 4.2 6.6 7 3.3 4.3 22 5.3 4.3 8 5.2 6.0 23 3.7 4.9 9 4.2 5.3 24 3.0 5.1 10 2.9 3.7 25 4.0 3.9 11 4.4 5.5 2.8 5.2 12 3.6 4.8 27 4.6 4.0 13 2.9 4.1 28 3.0 5.6 14 3.7 4.3 29 3.3 4.3 15 4.0 5.3 30 5.0 5.8 (a) Treat these samples as independent samples, one taken from the Brand A population and one taken from the Brand B population. At the a= 0.05 significance level, perform a hypothesis test to determine whether or not the mean drying times for the two brands of paints are different. To gain full credit, you should provide the following: i. Identify the parameters of interest, and the meanings in the context of this problem. ii. State and check the modeling assumptions that we have discussed in class. iii. State the null and alternative hypotheses, the test statistic, the rejection region, and the p-value. iv. Draw a conclusion based on your test statistic and the rejection region. Also use the p-value to draw a conclusion. Do these decisions correspond? If not go back and check your work. v. Interpret your conclusion in the context of the problem, (b) Calculate a 95 percent confidence interval for the population mean difference 21 - H2 and interpret your interval. Explain clearly in words) what i represents in the context of this problem.