thank you in advance:-
Show that ATE '] = or2, for each / = 1. 2. .... k. Hint. FIE, 3] = E ZE = Argue that due to the independence of the terms E, all cross-product terms E, E / # f. have expectation 0. Argue also that EL;] = or2.Let a = .05, and assume that all possible paired comparisons are to be made. For each value of k given in Exercise 12, use the Bonferroni procedure to find an upper bound for o', the overall probability of making at least one incorrect rejection. In each case, what level should be used to guarantee that o' s .10?Scientists concerned with treatment of tar sand wastewater studied three treatment methods for the removal of organic carbon. (Based on "Statistical Planning and Analysis for Treatments of Tar Sand Wastewater," W. R. Pirie, Technical Report, Virginia Tech University). The three treatment methods used were air flotation (A.F.), foam separation (F.S.), and ferric-chloride coagulation (F.C.C.). The organic carbon material measurements for the three treatments yielded the following data: A.F. F.S. F.C.C. 34.6 38.8 26.7 35.1 26.7 35.3 40 1 27.0 35.8 40.9 27,1 36.1 41.0 27.5 36.5 43.2 28.1 36.8 44.9 28.1 37.2 46.9 28.7 37.4 51.6 30.7 37.7 59.6 31.2 Test for differences among means. Be sure to report the P value of your test and state your conclusion.Show that I'M TUL IMExperiments were conducted to study whether commercial processing of various foods changes the concentration of essential elements for human consumption. One such experiment was to study the concentration of zinc in green beans. A batch of green beans was divided into four groups. The four groups were then randomly assigned to be measured for zinc as follows: group 1 measured raw, group 2 measured before blanching: group 3 measured after blanching; and group 4 measured after the final processing step. Independent measurements were taken from the four groups (treatments), yielding the following observations: Zinc concentration Group 1 Group 2 Group 3 Group 4 2.23 3.71 2.53 5.46 2 20 4.67 2.87 5.19 2.44 3.45 2.83 5.51 2.11 2.73 2.13 4.87 2.30 2.5H 2.19 6.63 1.72 1.85 1.80 2.39 1.78 1.81 1.75 2.09 2.16 2.32 1.83 2.27 2.91 2.50 1.97 2.39 (=) State the appropriate null and alternative hypotheses. (b) Test your hypothesis for significance at the 5% level. (c) Verbally state your conclusion.It was known that a toxic material was dumped in a river leading into a large salt water commercial fishing area. Civil engineers studied the way the water carried the toxic material by measuring the amount of the material (in parts per million) found in oysters harvested at three different locations, ranging from the estuary out into the bay where the majority of commercial fishing was carried out. The resulting data are given below: Site 1 Site 2 Site 3 15 19 22 26 15 20 10 24 20 26 26 29 11 15 28 17 21 13 24 26 15 18 (=) Test whether there is a significant difference in the average parts per million of toxic material found in oysters harvested at the three sites. Use o = .05. (b) Would the means be significantly different at the .01 level of significance? (Use a computer package to find the P value.) (c) Do your answers in parts (a) and (b) contradict each other? Justify your answer.As landfills begin to fill up and land for such operations becomes more scarce, recycling will become more and more necessary. Some fast-food chains have become aware of this problem and are beginning to use biodegradable packaging or to recycle their packaging material. A study is conducted to investigate the amount of money received per year for recycled goods by various sized businesses. These data, in thousands of dollars, are obtained (based on figures in "New Ways to Take Out the Trash," Tom Andel, Transportation and Distribution, May 1993): Company Size 101-250 251-500 Over 500 employees employees employees 3.5 3.8 13.4 14.1 9.0 10.5 3.4 3.0 - 14,0 14.7 10.3 10.7 3.7 2.8 14.5 15.0 10.1 9.5 3.3 3.2 14.7 13.6 10.6 11.2 20 3.0 15.2 143 104 9.7 2.6 41 15.5 14.6 10.5 10.0 3.5 4.0 14.2 14.8 103 11.3 4.2 49 15.3 15.6 10.7 11.8 ( ) Construct stem-and-leaf diagrams for each of these samples, and comment on the reasonableness of the normality assumption. (b) Estimate the variance of each of the populations from which these data are drawn, and comment on the reasonableness of the assumption of equal variances. (Do not try to test anything.) What has been done on this study to guard against a possible violation of the assumption of equal variances? (c) Test Ho: My = 12 = py. and report the P value of your test. What practical conclusion can be drawn?Scroll speed is an important consideration in the development of color graphics cards. A study is conducted to compare the time, in seconds, required to scroll one screen of WORD documents using five different color graphics cards with 24-inch monitors. The test conducted was a standard Hydra Quick Draw performance test. These data are obtained (based on information found in "Gauging Video Speed." MAC WORLD, June 1993, p. 28): Graphics cards C D 305 79.2 51.6 70.0 32.4 421 84.7 85.3 27.2 43.5 85.0 57.3 86.2 26.3 40.6 86.2 590 82.0 25,1 38.G JG.3 58.7 ST.2 38.2 32.1 83.1 6R.1 81.7 30.6 41.6 92.6 645 93.5 33.7 55 5 89.1 Use these data to test for equality of means. State your conclusion and report the P value of the test.Recall that MS- was defined as the ratio ($5_/(N - K). Show that F MS. = N- K for the one-way classification fixed-effects model.In Exercise 4, use Bartlett's test to determine whether it is reasonable to assume homogeneity of variances for the four treatment groups. If not, what type of alternative procedure is available to analyze these data?In each case determine the number of paired comparisons possible. (8) k = 3 (b) k = 6 (C) k = 10[Bonferroni inequality.) The following inequality provides the basis for determining the comparisonwise error rate needed to control the experimentwise error rate at some specified level. Let A. A,. .... A. be events. Then PAnAn . .nAJel-[PA)] + PAY + . . . + PLAY]] (=) Prove this result for c = 2. Hint Notice that by the general addition rule. PIA; UA'
