1.2. [2, 5]U[3, 7]=[2, 7]. EX LET x€[2,5]U[3,7]
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- Two new accessions of pepper were tested for pungency. The two accessions were given to ten persons who scored the pepper samples as 1 if it is the more pungent of the two and 0 , otherwise. Which test can be conducted to compare pungency of the two new accessions? a. F-test B. Friedman C. t-test D. sign testAt a certain school 60 of the 100 boys and 60 of the 80 girls signed up for the senior trip. Is there an associa-tion between going on the trip and gender? A) We can’t tell, because the class doesn’t have the samenumber of boys and girls.B) Yes, because the same number of boys and girlssigned up.C) Yes, because a lower percentage of boys signed upthan of girls.D) No, because the people on the trip were 50% boysand 50% girls.E) No, because the sign-up rate was higher among girlsthan among boys.A decision maker has a utility function for monetarygains x given by u(x) (x 10,000)1/2. a Show that the person is indifferent between the sta-tus quo and L: With probability 13, he or she gains $80,000 L: With probability 23, he or she loses $10,000b If there is a 10% chance that a painting valued at$10,000 will be stolen during the next year, what is themost (per year) that the decision maker would be willingto pay for insurance covering the loss of the painting?
- Ana’s preferences are consistent with expected utility. Denote by u(x) her utility function for a monetary outcome £x, and suppose that she is strictly risk-averse. Ana currently faces the monetary lottery which pays: £A with probability pA; £B with probability pB; and £C with probability pC. Now suppose that Ana is made the following o§er. For each realization of the original lottery, another lottery will be executed according to which she wins an additional poundwith probability 1/2 and loses a pound with probability 1/2. Describe the lottery that Ana faces if she accepts the o§er by describing the new payo§s and probabilities over these payo§s. (b) Show that she rejects the o§er and explain why.A manufacturing company employs two devices to inspect output for quality control purposes. The first device is able to accurately detect 99.3% of the defective items it receives, whereas the second is able to do so in 99.7% of the cases. Assume that four defective items are produced and sent out for inspection. Let X and Y denote the number of items that will be identified as defective by inspecting devices 1 and 2, respectively. Assume that the devices are independent. a)Determine E(X) b)Determine V(Y|X=2).Which of the following would be an appropriate decision rule when trying to support the alternative hypothesis that the population mean is greater than 45? (Assume α=0.10, n=16 and σ is unknown) Select one: a. reject the null hypothesis if t < -1.341 b. reject the null hypothsis if z < -1.28 c. reject the hull hypothesis if t >1.341 d. reject the null hypothesis if z >1.28
- The proportion of defective items is not allowed to be over 12%. A buyer wants to test whether the proportion of defectives in his shipment of 1000 items exceeds the allowable limit. The buyer takes a SRS of 100 items and finds that 19 are defective. State the null and alternative hypotheses for this test. Group of answer choices Ho: p = 0.12 vs Ha: p > 0.12 Ho: p = 0.19 vs Ha: p ≠ 0.12 Ho: p = 0.12 vs Ha: p < 0.19 Ho: p = 0.12 vs Ha: p = 0.19As a generalization of Example 5.3(figure), consider a test of n circuits such that each circuit is acceptable with probability p, independent of the outcome of any other test. Show that the joint PMF of X, the number of acceptable circuits, and Y, the number of acceptable circuits found before observing the first reject, is PX,Y(x,y) = ((n-y-1)C(x-y))*p^(x)*(1-p)^(n-x) For 0 ≤ y ≤ x < n p^(n) For x=y=n 0 otherwise Hint: For 0 ≤ y ≤ x < n, show that {X = x, Y = y} = A ∩ B ∩ C, where A: The first y tests are acceptable. B: Test y + 1 is a rejection. C: The remaining n − y − 1 tests yield x − y acceptable circuitsFind the highest possible value for x in the set 8.2 7.7 6 4.8 8.2 5.8 9.2 7.3 6.2 8.1 5.5 and x such that the mean of these scores is 7. show complete solution
- 5. To compare the gas mileage of 2 cars, you conduct 50 mileage tests on each of the 2 different cars. At α = 0.10, can you support the claim that car 1 gets better gas mileage than car 2. Data Car 1: µ = 28.3, s1 = 3.2 Car 2: µ = 28.7, s1 = 2.6 State the Ho, Ha, and the claim Group of answer choices Ho: m1 ≤ m2, Ha: m1 > m2 (claim) Ho: m1 ≥ m2 (claim), Ha: m1 < m2 Ho: m1 ≥ m2 , Ha: m1 < m2 (claim) Ho: m1 ≤ m2 (claim), Ha: m1 > m2Suppose N = 10 and r = 3. Compute the hypergeometric probabilities for the following values of n and x. n = 4, x = 1. n = 2, x = 2 n = 2, x = 0.1- Write all the possible cases ( x,y ) to distribute 6 distinguish particles in two rooms and the statistical probabilty ( w ) for each case. 2- Write all the possible cases ( x,y ) to distribute 8 distinguish particles in two rooms and the statistical probabilty ( w ) for each case. 3- how many possible cases ( x,y ) distribute 8 distinguish particles in four rooms? Write five different cases and the statistical probabilty ( w ) for each