probability expert required here.

\fThe method of Xray uorescence is an important analytical tool for determining the concentration of material in solid missile propellants. In the paper An Xray Fluorescence Mewd forAnalyzing PotybutadieneAcqtchud {PEAAJ Propellants {Quarterly Report, RKTREEl Amy Ordinance Missile Command, 1962], it is postulated that the propellant mixing process and analysis time have an inuence on the homogeneity of the material and hence on the accuracy of illray intensity measurements. An experiment was conducted using 3 factors: A, the mixing conditions conditions {4 levels}; B, the analysis time {2 levels}; and G, the method of loading propellant into sample holders [hot and room temperature]. The following data, which represent the weight percent of ammonium perchlorate in a particular propellant, were recorded. {a} Perform an analysis ofyan'anee with o = {101 to test for significant main and interaction effects. {b} Discuss the influence of the three factors on the weig'lt percent of arrmonium percl'rlorate. Let your discussion involve the role of any sign'rlicant interaction. For a study of the hardness of gold dental fillings, five randomly chosen dentists were assigned combinations of three methods of condensation and two types of gold. The hardness was measured. (See Hoaglin, Mosteller, and Tukey, 1991.) Let the dentists play the role of blocks. The data are presented here. (a) State the appropriate model with the assumptions. (b) Is there a significant interaction between method of condensation and type of gold filling material? (c) Is there one method of condensation that seems to be best? Explain Type Dentist Method Gold Foil Goldent 1 792 824 772 772 782 803 2 803 803 752 772 715 707 (cont.) Type Dentist Method Gold Foil Goldent 3 715 724 09 19 P 792 715 762 606 4 673 946 09 19 ) 657 743 690 245 5 634 715 09 19 # 649 724 724 627Electronic copiers matte copies by gluing olaclt inlt on paper, using static electricity. Heating and gluing the inlt on the paper comprise the nal stage ofthe copying process. The gluing power during this nal process determines the gualil'jnr of the copy. It is postulated that temperature, surface state of the gluing roller. and hardness of the press roller inuence the gluing power of the copier. An experiment is mn with treatments consisting of a combination of these three factors at each of three levels. The following data show the gluing power for each treatment combination. Perform an analysis of iraria nce with o = {105 to test for signicant main and Surface State of Hardness of the Gluing Press Roller Roller [1.52 Su: Law interaction EEE'IS. (1.44 [L43 [1.27 [LET Consider combinations of three factors in the removal of dirt from standard loads of laundry. The first factor is the brand of the detergent, X, Y, or Z. The second factor is the type of detergent, liquid or powder. The third factor is the temperature of the water, hot or warm. The experiment was replicated three times. Response is percent dirt removal. The data are as follows: Brand Type Temperature X Powder Hot 85 88 80 Warm 82 83 85 Liquid Hot 78 75 72 Warm 75 75 73 Y Powder Hot 90 92 92 Warm 88 86 88 Liquid Hot 78 76 70 Warm 76 77 76 Z Powder Hot 85 87 88 Warm 76 74 78 Liquid Hot 60 70 68 Warm 55 57 54 (a) Are there significant interaction effects at the a = 0.05 level? (b) Are there significant differences between the three brands of detergent? (c) Which combination of factors would you prefer to use?A scientist collects experimental data on the radius of a propellant grain, y, as a funciion of powder temperature, extrusion rate, and die temperature. Results of the threefactor experiment Powder Temp 152 122 . [he 'IEmp Dle 'Iemp are \"mm" Rate W W 12 22 121 22 122 24 114 122 121 124 Resources are not available to make repeated experimental trials at the eight combinations of factors. It is believed that extrusion rate does not interact with die temperature and that the three factor interaction should be negligible. Thus, these two interactions may be pooled to produce a 2 d.f. \"error" term. {a} Do an analysis of 1.rariance that includes the three main effects and two two-factor interactions. Determine what effects influence the radius ofthe propellant grain. {b} Consbuct interaction plots for the powder temperature by die temperature and powder temperature by exthsion rate interactions. {c} Comment on the oonsistency in the appearanoe of the interaction plots and the tests on the two interactions in the ANDVA. In the book Design of Experiments for Dualihr Improvement, published by the Japanese Standards Association (1959), a study is reported on the extraction of polyethylene by using a solvent and how the amount of gel {proportion} is inuenced by three factors: the type of solvent, extraction temperature, and extraction time. Afactonal experiment was designed, and the following data 1were collected on proportion of gel. Time 91.9 94.9 91.1 99.5 95.3 95.1 94.9 95.3 92.5 92.4 Toluene 120 9-1.6 94.5l9. 94.1 91.1 91.9 391ml". Teonp. 39 95.4 95.4 95.5 96.9 92.1 92.1 {a} [to an analysis of variance and determine what factors and interactions inuence the proportion of gel. {b} Consimct an interaction plot for any twofactor interaction that is signicant. In addition, explain what oonclusion can be drawn from the presence ofthe interaction. {c} Do a normal probability plot of residuals and comment. \fAn experiment WES conducted in the Department pf Fddd Science at Virginia Tech. it was of interest to characterize the texture of certain types of sh in the herring family. The effect of sauce types used in preparing the sh was also studied. The response in the experiment was \"texture value,\" measured 1llilith a machine that sliced the sh prod uct. The fdlldwing are data an tethre yalues: {a} Do an analysis dfyariance. Determine 1whether or not there is an interaction between sauce type and sh type. {b} Based on ypur results from part {a} and en Ftests on main effects, determine if there is a signicant diffe renee in texture due to sauce types, and determine whether there is a signicant difference due to sh types. \f