PROBLEM 1 – TESTING PAINT BRAND CLAIMS

Situation:

Does a paint brand matter? Four different paint brands advertised for the same type of paint that they have the same drying time. To check the manufacturer’s claims, five 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.

Action:

Use the following data and ANOVA to test whether there is a significant difference in mean drying time among the paint brands. Use significance level of 5%. Discuss the business implications of the findings.

a. SHOW THE Ho AND Ha APPROPRIATE FOR THIS PROBLEM

b. WHAT IS THE P-VALUE FOR THIS PROBLEM?

c. COMPARE P-VALUE TO PROBLEM STATEMENT SPECiFIED SIGNIFICANCE VALUE AND STATE WHETHER Ho SHOULD OR SHOULD NOT BE REJECTED

d. BASED ON WHETHER Ho IS REJECTED/NOT REJECTED, STATE WHETHER THERE IS A SIGNIFICANT DIFFERENCE IN AVERAGE DRYING TIMES.

For the next two parts of the problem, run a Post-Hoc Comparison's test on the four means to answer. You can select whichever Post-Hoc Comparison procedure you want.  If none exists on your software, do individual t-tests on all pairs of means.  Options for post-hoc test: test of hypothesis comparing two population means, Tukey method, or any other pairwise comparison test.

a. WHAT POST-HOC COMPARISON TEST USED?

b. SHOW THE Ho AND Ha FOR EACH PAIRWISE TEST, SHOW THE RELEVANT STATISTICS (i.e. FOR TEST OF HYPOTHESIS COMPARING TWO POPULATION MEANS SHOW THE p-VALUE AND DISCUSS WHETHER Ho IS REJECTED AND THE IMPLICATION OF REJECTING THE Ho. IF TUKEY’S METHOD USED SHOW ALL RELEVANT STATISTICS TO SUPPORT THE CONCLUSIONS).  STATE THE CONCLUSION DRAWN BASED POST-HOC COMPARISON TEST COMPLETED.