Question

Yellow stains on white clothing are stubborn discolorations believed to result from oxidated body oils that have reacted chemically with clothing’s cellulose fibers (as if it were a dye). In as little as one week, there reaction can permanently discolor with clothing with an ugly yellow stain and at this point the most potent laundry product will usually be of little value in removing them. Suppose researchers at the Department of Textiles and Apparel at Cornell University, experimenting with new experimental formulations to remove stains, washed six discolored strips in each of three experimental formulations, and the results as follows Coloring rating (after washing) 0 = Dark Yellow, the initial shade 20 = Pure White-All washed strips were matched to a color chart, a series of increasingly lighter shade, and rated from 0 to 20. Formulation X Y Z 10 8 11 9 10 12 10 12 14 12 9 11 8 10 10 11 8 14 Three Different Formulations were tested a) Calculate by hand the average color rating and variance for each group b) Assuming valid random samples, test at 5% level significance whether differences among the three-sample means can be attributed to chance fluctuation or, indeed, to actual differences in the stain-eliminating ability of the three formulations. ( hint: find the F-ratio) c) Briefly discuss the implications of these results. Need to solve by hand. Please help!

Answer 1

Now it is not required to answer the following in the question. But you check the difference among means for each pair of formulation to know which means are different to one another. The test statistics for each case is Fisher's t-test. The test statistics is given by:

where and   and are respectively sample mean for group 1 and group 2 and and are respectively sample variance for group 1 and group 2. Calculate the values of the test statistics for each three testing and compare with the critical value of . If then reject null and conclude that the pair of means is significantly different at 5% level of significance.