Let X be a single observations from density S7 0
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![- Let X be a single observations from density
0 < x < 1
f(x; 0) = {
else
(a) Let Y = -(log X)-1. Evaluate the confidence coefficient of the set
[y/2, y). [Answer:0.239]
(b) Find a pivotal quantity and use it to set up a confidence interval having
the same confidence coefficient as the interval in part (a). [Answer: Xº ~](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9ff65e7f-3474-4cde-87a4-83d678c8ef48%2Fd9a4ef9f-cc05-49a4-8135-3884f4b51f92%2F6aq6z70w_processed.png&w=3840&q=75)
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- An economic instructor at UCF is interested in the relationship between hours spent studying and total points earned in a course. Data collected on 19 students who took the course last semester follow # of observation(s) n = 19 # of independent variable(s) = 1 SSR = 3,882 SSE = 256 Find the Value for MSE (Use two decimals)Consider independent observations (rı, y1), ... (rns yn), from the model Y, Bin(ri, p) for i = 1, ... , n, where the r, are fixed constants. Using likelihood L(p) and log-likelihood I(p) as appropriate, compute the following items. N 1. Derive the maximum likelihood estimate p. 2. Write the second derivative of log-likelihood /(p). == 3. Give an expression of the approximated asymptotic standard error of p by plugging in the estimate p. To this end, estimate the Fisher Information Matrix by : and then s. e. ap² 4. Consider data (15,11), (20,14), (15,9), (10,7), (25,17), (15,12), (10,8). Using your formulæ, compute and write numerical estimates p, s. e. (p) and give a 95% confidence interval for p using the normal approximation. e. (p) = √v¹¹ p=p Note: To answer this question you will work by hand. Do not write in the textbox but upload a single page pdf image of your workings and results. For theoretical computations (a) to (c) you are expected to show your equations and developments…According to the Institute of Medicine, the tolerable upper level of sodium intake for adults and adolescents is 2300 mg per day. A researcher believes that adolescents in the United States consume sodium in excess of the tolerable upper level. (a) µ represents the population mean adolescents in the United States. (b) State the hypotheses (Ho & Ha) for a test to verify the researcher's belief. Then, state what the parameter µ in your hypotheses is. of
- Please help to solve this and explain into detial. Thank youQ2. (a) Suppose that X B(n=10, p) and consider the point estimate. Let us consider = X as 12 a point estimate of p. X an unbiased point estimate of p? Justify your answer. 12. i) Is p =- X What is the mean square error of p= 12 ii) b) Suppose that, E(X)= E(Y)= µ, Var(X)= 4, and Var(Y) = 6. What value of p minimizes the variance of u= pX +(2- p)Y? .Find the MSE of û. MAT361SSFinSp22.docxα = 0.01 for a right tailed test. Find the critical z value.
- For 50 randomly selected speed dates, attractiveness ratings by males of their female date partners (x) are recorded along with the attractiveness ratings by females of their male date partners (y); the ratings range from 1 to 10. The 50 paired ratings yield x = 6.2, y = 6.0, r=-0.209, P-value = 0.144, and y=7.48 -0.239x. Find the best predicted value of ŷ (attractiveness rating by female of male) for a date in which the attractiveness rating by the male of the female is x = 4. Use a 0.05 significance level. The best predicted value of y when x = 4 is (Round to one decimal place as needed.) CFor 50 randomly selected speed dates, attractiveness ratings by males of their female date partners (x) are recorded along with the attractiveness ratings by females of their male date partners (y); the ratings range from 1 to 10. The 50 paired ratings yield x-6.4, y= 6.1, r= - 0.226, P-value = 0.115, and y = 7.81 - 0.269x. Find the best predicted value of y (attractiveness rating by female of male) for a date in which the attractiveness rating by the male of the female is x= 6. Use a 0.10 significance level. The best predicted value of y when x= 6 is (Round to one decimal place as needed.)An experiment is conducted to compare the maximum load capacity in tons (the maximum weight that can be tolerated without breaking) for two alloys A and B It is Kknown that the two standard deviations in load capacity are equal at 7 tons each. The experiment is conducted on 50 specimens of each alloy (A and B) and the results are X = 75.8. X = 71.8, and X-X=4. The manufacturers of alloy A are convinced that this evidence shows conclusively that Hug and strongly supports the claim that their alloy is superior. Manufacturers of alloy 8 claim that the experiment could easily have given X-X 4 even if the two population means are equal. Complete parts (a) and (b) below. Click here to view page 1 of the standard normal distribution table. Click here to view page 2 of the standard normal distribution table. (a) Make an argument that manufacturers of alloy B are wrong. Do it by computing P(XA-XB41 PA-HB) P(XA-X > 4) - @
- Find the positive critical t -value for a two tailed test with a = answer to 3 decimal places. 0.05 and df = 11. Give yourSuppose f(x) = 1/20 from 5 to 25. What is the 25th percentile of X? 10 1/20 None of the other choices is correct .25For a hypothesis test of the claim that the mean amount of sleep for adults is less than 6 hours, technology output shows that the hypothesis test has power of 0.4733 of supporting the claim that μ<6 hours of sleep when the actual population mean is 4.0 hours of sleep. Interpret this value of the power, then identify the value of β and interpret that value.
