Main effect Factor A=(45+10+40+8)/4-(8+47+41+8)/4=-0.25B= (47+10+41+8)/4-(8+45+8+40)4=1.25Interaction=(8+47+40+8)/4-(45+10+8+41)/4=-0.25C) Sum(y+)/n+=(8+45+47+10)/4=27.5 and Sum(y-)/n-=(8+40+10+8)/4=24.510 88 827.5 24.5414745 40+ + + math Experiment代写(a) Suppose the three real estate appraisers independently examined each of five properties chosen atrandom from a particular neighborhood and gave appraised values. The manager of the appraisalservice that employs them suspects that systematic differences among their methods of appraisalare causing undesirable inconsistencies in appraised values provided by her service. The issueis whether there are, in fact, systematic differences among the values reported by the threeappraisers. The data, APPRAISED VALUES (In thousands of dollars), are shown below.Question: What kind of statistical analysis should you perform? Choose from: (Two sample ttest,pairwise t-test, One-way ANOVA, One-way ANOVA with block, Two-way ANOVA, Factorialdesign). If your answer is One-way ANOVA with block, which variable does play a role of block?AppraiserProperty A B C1 90 93 922 94 96 883 91 92 844 85 88 835 88 90 87(b) Suppose each of 4 Chardonnay wines of the same vintage was judged by 5 judges. Each wine wasblinded and given to each judge in randomized order. The wines were scored on a 40-point scale,with higher scores meaning better wine. Based on those scores, we want to test whether there isa difference between the 4 Chardonnay wines in mean scores.Question: What kind of statistical analysis should you perform? Choose: (Two sample t-test,pairwise t-test, One-way ANOVA, One-way ANOVA with block, Two-way ANOVA, Factorialdesign). If your answer is One-way ANOVA with block, which variable does play a role of block?1(c) A researcher was interested in whether an individual’s interest in politics was influenced by theirlevel of education and gender. Therefore, the dependent variable (response variable) was “interestin politics” and the two independent variables were “gender” and “level of education.”In particular, the researcher wanted to know whether there was an interaction between educationlevel and gender. Put another way, was the effect of level of education on interest in politicsdifferent for males and females?To answer this question, a random sample of 60 participants were recruited to take part in thestudy–30 males and 30 females–equally split by level of education: school, college and university(i.e., 10 participants in each group). Each participant in the study completed a questionnairethat scored their interest in politics on a scale of 0 to 100, with higher scores indicating a greaterinterest in politics.Question: What kind of statistical analysis should you perform to answer for the original question?(Two sample t-test, pairwise t-test, One-way ANOVA, One-way ANOVA with block, Two-wayANOVA, Factorial design)Answer:a)one way anova c) two way anova####building matrix for conveniencea - matrix(c(90,94,91,85,88,93,96,92,88,90,92,88,84,83,87),nrow=5,ncol=3)A - a[,1]B - a[,2]C - a[,3]####combine datacombine - data.frame(cbind(A,B,C))combinesummary(combine)stack.comb - stack(combine)stack.combpropo - c(1,2,3,4,5)###anovaanva - aov(values~ind,data = stack.comb)summary(anva)comb2 - cbind(stack.comb,propo)propo1 - rep(propo,3)comb2anva2 - aov(values~ind+propo1,data=stack.comb)anva2 anvaCall:aov(formula = values ~ ind, data = stack.comb)Terms:ind ResidualsSum of Squares   62.8     132.8Deg. of Freedom     2        12Residual standard error: 3.32666Estimated effects may be unbalanced anva2Call:aov(formula = values ~ ind + propo1, data = stack.comb)Terms:ind propo1 ResidualsSum of Squares  62.8   58.8      74.0Deg. of Freedom    2      1        11Residual standard error: 2.593699Estimated effects may be unbalancedB) two sample t test t.test1 -  t.test(a2,b2,alternative = two.sided , var.equal = FALSE) t.test2 - t.test(a2,c2,alternative = two.sided , var.equal = FALSE) t.test3 - t.test(b2,c2,alternative = two.sided , var.equal = FALSE) t.test1Welch Two Sample t-testdata:  a2 and b2t = -2.0327, df = 27.709, p-value = 0.05177alternative hypothesis: true difference in means is not equal to 095 percent confidence interval:-4.41809197  0.01809197sample estimates:mean of x mean of y89.6      91.8 t.test2Welch Two Sample t-testdata:  a2 and c2t = 2.391, df = 27.905, p-value = 0.02379alternative hypothesis: true difference in means is not equal to 095 percent confidence interval:0.4007834 5.1992166sample estimates:mean of x mean of y89.6      86.8 t.test3Welch Two Sample t-testdata:  b2 and c2t = 4.4696, df = 27.303, p-value = 0.0001239alternative hypothesis: true difference in means is not equal to 095 percent confidence interval:2.705863 7.294137sample estimates:mean of x mean of y91.8      86.8Recall the comparison between factorial design and one-factor-at-a-time (OFAT) approach considered in class: In the 22 factorial design (without replications), we conduct a total of 4 runs. The main effects of both factors (say A and B) are estimated by the difference between averages of two observations at the low and the high levels of each factor. Therefore, in order for the OFAT to achieve the same level of precision (that is, to obtain averages of two), one must have 2 runs at each experimental combination. Hence, for the 2 factor case, OFAT requires 2 × 3 = 6 total runs whereas 22 factorial design needs 2 2 = 4 runs. Now, suppose there are 5 factors (A, B, C, D, E), each having two-levels. We know 25 factorial design (without replications), we conduct a total of 32 runs. How many total runs are required in order for the OFAT approach to achieve the same precision? Explain why.Answer:Since this is 2^5 factorial OFAT approach needs 96 runs to achieve the similar result. In OFAT approach, we need to change one factor at a time. When change the a factor level, others remains the same. When it comes to 2 factorial design, it needs 4 runs while OFAT is 6. In Three factors it takes 2^3 runs, and 16 runs in OFAT. For 4 factorial design, it needs 2^4=16 runs and 40 runs for OFAT. So 2,4,6. 3,8,16. 4,16,40. We can conclude that it need 2^(n-1) *(n+1) times OFAT so 5 factors needs 96 runs.最先出自315代写 Latex代写 数学代写合作：315代写

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