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involving the outcomes of an experiment. For this problem, assume that S={O1,O2,O3,O4,O5} and that w1=0.29, w2=0.2, w3=0.04, w4=0.14, w5=0.33. Let E={O5,O1} and F={O3,O4}.
(1) What is the value of Pr[E]?
(2) What is the value of Pr[F′]?
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- Test the claim that 73% of women shoppers remained loyal to their favorite supermarket in the last year. In a random sample of 610 women shoppers, 417 remained loyal to their favorite supermarket last year. Use α=0.01.Q3 A researcher wish to compare four manufacturing methods on the breaking strength of plastic. Four types of machines are used in this experiment. He believed that machines have an effect on the plastics breaking strength. However, each machine can operate only three methods during the experiments on a given day. Table Q3 shows the data of the experiment. Table Q3: Four manufacturing methods on the breaking strength of plastic Manufacturing Methods Machine 2 1 A=73 C=73 D=75 2 A=74 B=75 C=75 3 B=67 C=68 D=72 4 A=71 В-72 D=75 What is the name of the design? Write an appropriate statistical model then list the assumptions and identify the terms. (a) (b) Is this design symmetric ? Justify your answer. State if the design balance or not. Discuss how to achieve balance in this design ? Justify your answer. (c) (d) Test the hypothesis at a = 0.05 whether there is an effect of the four manufacturing methods on the breaking strength of plastics.Q-4)Show all the steps for the problem.
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- Assume that W (t) is a standard Brownian motion and that S(t) is a random variable defined as S(t) = 8 · 2W(t). Determine(2.1)Biologists in Minnesota are interested in determining if there is a difference in the invasion rate of Asian Carp (which can be detrimental to the environment) between the Mississippi River and Lake Mille Lacs. In the Mississippi River, it was found that 206 of 579 fish caught were Asian Carp. In Lake Mille Lacs, 28 of 132 fish caught were Asian Carp. Let p, = the true proportion of Asian Carp in the Mississippi River and let p2 = the true proportion of Asian Carp in Lake Mille Lacs. A test of Ho: P₁ = P2 vs. Ha: P₁ P₂ resulted in a p-value of 0.0015. Which of the following is a correct conclusion? (A) The test is not appropriate, since the researchers should have conducted a one-sided test. (B) The test is not appropriate, since the sample size is too small to conduct an inference test for proportions. (C) The test is not appropriate, since the two sample sizes are very different. (D) The p-value of this test is large, indicating we have sufficient evidence to conclude that a…