: 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.

1. Treat these samples as independent samples, one taken from the Brand A populationandonetakenfromtheBrandBpopulation.Atthe?= 0.05significance 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 providethe following:
   1. Identify the parameters of interest, and the meanings in the context of this problem.
   2. Stateandcheckthemodelingassumptionsthatwehavediscussedinclass.
   3. State the null and alternative hypotheses, the test statistic, the rejection region, and the p-value.
   4. 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.
   5. Interpretyourconclusioninthecontextoftheproblem.
   6. Calculatea95percentconfidenceintervalforthepopulationmeandifference₁?₂ and interpret your interval.Explain clearly (in words) what represents in the context of this problem.

Specimen Brand A Brand B Specimen Brand A Brand B 3.5 4.7 16 5.2 6.2 2.7 3.9 17 4.0 5.1 3.9 4.5 18 4.1 5.4 4.2 5.5 19 3.4 4.8 4.6 4.0 20 3.3 4.9 10 0 - a UA WN 2.7 5.3 21 4.2 6.6 3.3 4.3 22 5.3 4.3 5.2 6.0 23 3.7 4.9 4.2 5.3 24 3.0 5.1 2.9 3.7 25 4.0 3.9 11 4.4 5.5 26 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