9. Consider the following two step experiment: Step1: we toss a coin (can land H or T) with P(H) = 0.6 - Step 2: If the coin lands H we roll a fair 4-sided die with labels 1, 2, 3, 4 Else we roll a die with distribution 1 2 3 4 0.2 0.3 0.2 0.3 Let E = Die rolls to an even number, and F = Coin lands H. (a) Draw the labelled tree diagram for this experiment. (b) List out all outcomes in the sets E and F. (c) Calculate P(E), P(F), P(E|F). (d) Are the events E and F independent? Show all work.
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- If a binomial experiment has probability p success, then the probability of failure is ____________________. The probability of getting exactly r successes in n trials of this experiment is C(_________, _________)p (1p)What is an experiment?Suppose that you plot the residuals for your sample and get Figure 2. You should conclude that Select one: a. possibly homoskedastic and you would perform a correction for homoskedasticity. b. likely homoskedastic. c. possibly heteroskedastic and you would perform a formal test for heteroskedasticity. d. definitely heteroskedastic.
- Q.No.2. An experiment was performed with seven hop plants. One half of each was pollinated and the other was not pollinated. The yield of the seed of each hop plant is tabulated as follows. Plant 1 3 5 7 number pollinated 0.78 0.76 0.43 0.92 0.86 0.59 0.68 Non- 0.21 0.12 0.32 0.29 0.30 0.20 0.14 pollinated a: Determine at the 5 per cent level whether the pollinated half of the plant gives a higher yield in seed than the non-pollinated half by 5 percent. State the assumptions and hypotheses to be tasted and carry through the computations to make decision. Justify the method you applied. b: Compute 90%confidence limits for the difference plants in mean yields. How would your explanation change if 99% confidence interval used instead? c: Use confidence limits to support the result obtained in part a.10. Professor Snape is your instructor for Chemistry 101. He has given the same final exam for his class for a long time; he happens to know that exam scores on this test are normally distributed and have a population mean of µ=80. Because of prior laboratory catastrophes (don’t worry, all students were returned to their original species), he tried a new method of instruction this year. He got a random sample of n=16 students and taught them using virtual reality. These students then took his original final exam, and their sample average was M=76. --------unique information for the second question below: -------- Assume for this second question that Snape’s final exam has a population standard deviation of σ=6. Can he demonstrate that the virtual reality instruction method was significantly different from his traditional teaching method? (Assume a two-tailed test with α=.05) Yes, he can conclude that his VR method is significantly different from his traditional…O IV. None of these QUESTION 2 Question 11. (HEALTH IS WEALTH) A health conscious squirrel joined a gymnasium to run a treadmill in the month of April. At the end of the month, she noted the average mileages for a random sample of seven days is: x = 4.5 miles. She is worried to know how many miles should she run today so that her average mileage for 8 days becomes 5 miles. QUESTION 3 Question 8
- 8. Professor Snape is your instructor for Chemistry 101. He has given the same final exam for his class for a long time; he happens to know that exam scores on this test are normally distributed and have a population mean of µ=80. Because of prior laboratory catastrophes (don’t worry, all students were returned to their original species), he tried a new method of instruction this year. He got a random sample of n=16 students and taught them using virtual reality. These students then took his original final exam, and their sample average was M=76. Assume for this third question that Snape’s final exam has a population standard deviation of σ=2. Can he demonstrate that the virtual reality instruction method was significantly different from his traditional teaching method? (Assume a two-tailed test with α=.05) Yes, he can conclude that his VR method is significantly different from his traditional method. This is because the z-test equals -4.00 and is significant…Random collections of nine different solutions of a calcium compound were given to two laboratories, A and B. Each laboratory measured the calcium content (in mmol per liter) and reported the results. The data are paired by calcium compound. Compound 1 2 3 4 5 6 7 8 9 Lab A (x) 12.35 9.83 10.79 11.31 8.58 13.69 14.68 15.07 11.57 Lab B (y) 12.18 9.72 10.70 11.51 8.63 13.58 14.71 15.24 11.57 (a) Rank-order the data using 1 for the lowest calcium reading. Make a table of ranks to be used in a Spearman rank correlation test. Compound Lab A (x) Lab B (y) d = x − y d2 1 2 3 4 5 6 7 8 9 Σd2 = (b) Use a 5% level of significance to test for a monotone relation (either way) between ranks. Interpret the results. What is the level of significance? Compute the sample test statistic. (Round your answer to three decimal places.)5. Professor Snape is your instructor for Chemistry 101. He has given the same final exam for his class for a long time; he happens to know that exam scores on this test are normally distributed and have a population mean of µ=80. Because of prior laboratory catastrophes (don’t worry, all students were returned to their original species), he tried a new method of instruction this year. He got a random sample of n=16 students and taught them using virtual reality (VR). These students then took his original final exam, and their sample average was M=76. Assume for this first question that Snape’s final exam has a population standard deviation of σ=12. Can he demonstrate that the VR instruction method was significantly different from his traditional teaching method? (Assume a two-tailed test with α=.05) No, he cannot conclude that his VR method is significantly different from his traditional method. This is because the z-test equals -1.00 and is not significant…
- A14c.. Answers must be in 4 decimal places with correct units and complete solutions.1. Consider the following information about random variables X, Y, A, and B: Hx = 30 %3D Ox = 10 Hy = 40 Oy = 20 A = 0.6X + 0.4Y B = 0.8X – 0.2Y Suppose that pxy = 0.2. What is o4? Round your final answer to four decimal places if necessary.