The proportion of rats that successfully complete a designed experiment (e.g., running through a maze)is of interest for psychologists. Denote by Y the proportion of rats that complete the experiment, andsuppose that the experiment is replicated in 10 different rooms. Assume that Y₁, Y2,..., Y10 are i.i.d.Beta random variables with a = 2 and B = 1. Recall that for this Beta model, the pdf isfy(y)=J2y if 0 0.9).

a) fY(10)(y)=20y19;0<y<1 =0;otherwise b) P(Y10 > 0.9) =…

Answered: The proportion of rats that…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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41
An automobile dealer conducted a test to determine if the time in minutes needed to complete a minor engine tune-up depends on whether a computerized engine analyzer or an electronic analyzer is used. Because tune-up time varies among compact, intermediate, and full-sized cars, the three types of cars were used as blocks in the experiment. The data obtained follow. Analyzer Computerized Electronic Compact 50 41 Car Intermediate 56 44 Full-sized 62 47 Use a = 0.05 to test for any significant differences. State the null and alternative hypotheses. O Ho: Hcompact * HIntermediate * HFull-sized Ha: "Compact = HIntermediate = 4Full-sized O Ho: HComputerized * HElectronic Ha: HComputerized = HElectronic O Ho: HComputerized = HElectronic Ha: "Computerized * HElectronic O Ho: HComputerized = HElectronic = "Compact = HIntermediate = "Full-sized H.: Not all the population means are equal. O Ho: HCompact = HIntermediate = HFull-sized Hai H compact * HIntermediate * HFull-sized Find the value of…
The Pearson correlation between X and Y is r = 0.40. When a second variable, X₂, is added to the regression equation, we obtain R2 = 0.64. How much variance for the Y scores is predicted by using both X and X₂ as predictor variables? O 0.40 or 40% O 0.64 or 64% O 0.48 or 48% O 0.16 or 16%
The following sample contains the scores of 6 students selected at random in Mathematics and English. Use the scores in English as the dependent variable Y. Mathematics score (X) 70 92 80 74 65 83 English score (Y) 74 84 63 87 78 90 ∑x=464, ∑y=476,∑x^2=36354,∑y^2=38254, ∑xy=36926. Estimate the regression parameters and also write the prediction equation.
16.17 In an experiment comparing four diets (treatments), the weight gain y (pounds per day) of pigs was recorded along with two covariates, initial age x₁ (days) and initial weight x2 (pounds). The data are presented in Table 16.11. (a) Using (16.67), (16.68), and (16.69), find Ex, exy, and eyy. Find B. (b) Using (16.77), (16.81), and (16.82), find SSEyr, SST.x, and SS(alu, B). Then test Ho: a₁ = ₂ = a3 = a4, adjusted for the covariates, using the F statistic in (16.83). (c) Test Ho: B = 0 using (16.84). (d) Find B₁, B₂, B3, and 4 using (16.88). Find SSE(F), and SSE(R)y.x using (16.86) and (16.87). Test Ho: B₁ B₂ B3 B4 using (16.89). X1 X2 y X1 78 61 1.40 78 90 59 1.79 99 94 76 1.72 80 71 50 1.47 75 1.26 94 1.28 91 1.34 75 1.55 63 1.57 62 1.26 TABLE 16.11 Initial Age x₁, Initial Weight x2, and Rate of Gain y of 40 Pigs Treatment 1. Treatment 2 Treatment 3 Treatment 4 99 61 80 54 83 57 75 45 62 41 67 40 X2 y X1 74 1.61 78 75 1.31 83 64 1.12 79 48 1.35 70 1.29 85 1.24 83 1.29 1.43 1.29…
Suppose an experiment finds that people taking a new herbal remedy get fewer colds than people taking a placebo. The results are statistically significant at the 0.01 level. Has the experiment proven that the herbal remedy works?
Q7. Many manufacturing companies in the United States and abroad use molded parts as components of a process. Shrinkage is often a major problem. Thus, a molded die for a part is built larger than nominal size to allow for part shrinkage. In an injection molding study it is known that the shrinkage is influenced by many factors, among which are the injection velocity in ft/sec and mold temperature in ◦C. The following two data sets show the results of a designed experiment in which injection velocity was held at two levels (low and high) and mold temperature was held constant at a low level. The shrinkage is measured in cm × 104. Shrinkage values at low injection velocity: 72.68, 72.62, 72.58, 72.48, 73.07, 72.55, 72.42, 72.84, 72.58, 72.92 Shrinkage values at high injection velocity: 71.62, 71.68, 71.74, 71.48, 71.55, 71.52, 71.71, 71.56, 71.70, 71.50(a) Construct a dot plot of both data sets on the same graph. Indicate on the plot both shrinkage means, that for low injection velocity…

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