Q 8. You fit a Pareto distribution to a sample of 200 claim amounts and use the likelihood ratio test to test the hypothesis that a = 1.5 and 0 = 7.8. You are given: (i) The maximum likelihood estimates are a = 1.4 and @= 7.6. (ii) The natural logarithm of the likelihood function evaluated at the maximum likelihood estimates is -817.92. (iii) Eln (x + 7.8) = 607.64. Determine the result of the test.
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- We are trying to predict GPA (Y) using number of hours spent studying (X1) and gender (X2). Our indicator variable for gender with male as the base is: If = {1 if Female} {0 else Our model is Y = Bo + B1X1+ B2IF + 8 } What is the expected value of Y if gender is female? O HF = Bo + B1X1 O µF = 0 O HF = Bo + 1 O uF = Bo + B1X1 + B23. Time intervals (in minutes) X₁,..., Xn between successive eruptions of a geyser are modeled as X₂ Exponential (A), where A (> 0) is the eruption rate per minute. We want to report a plausible range for the median interval time. (d) 0 Find the MLE of A. (b) (c) Construct an approximate 95% confidence interval for A using the asymptotic distri- bution of AMLE. (Hint: use the approximation method for confidence interval) i.i.d. N = The median of the Exponential(A) distribution, denoted by 8, is a function of A as (log 2)/λ 0.693/A. Calculate an approximate 95% confidence interval for the median interval time using the Delta method. Find the Fisher information of A. -Can you show me how to calculate this? A random sample of 24 items is drawn from a population whose standard deviation is unknown. The sample mean is x¯ = 880 and the sample standard deviation is s = 5.s replaces a; t replaces z(a) Construct an interval estimate of μ with 99% confidence. (b) Construct an interval estimate of μ with 99% confidence, assuming that s = 10. (c) Construct an interval estimate of μ with 99% confidence, assuming that s = 20.
- You flip an unfair coin with Pr[H]=0.2 three times. Find the expected number of heads flipped.One consumer wants to know if the average number of chips is less than 45 in a bag of Red Bird potato chips. A random sample of 100 was selected and the sample statistics werex=41.6 and s = 7.6. (i) What is the standard error of x? (ii) Using one or two sentences, briefly describe the Central Limit Theorem (CLT) for the sample mean. (ii) Does CLT hold for this test? Explain your reasoning. (iv) State the hypotheses for the test. (v) Give a 90% CI (3 d.p.) for the average amount of chips in each bag (The margin of error is 1.262). (vi) Interpret your Cl in part (iv) in context. (vii) Make a decision and conclusion based on your Cl in part (v).ACT is normally distributed with µ = 21.0 and σ = 5.5. What proportion of students who took ACT and scored between 18 and 28, P(18 < X < 28)? -I calculated the Z scores from 18 and 28, do I take those scores then use the Z table? would the answer be P( .2946 < X < .8980) ? Not sure if I'm doing the right steps here
- The distance, X, between flaws on a long cable has an exponential distribution with a parameter λ = f(x, 2) = 2 e-ix for 0 ≤ x ≤ 00, λ = 12 a) What is the expected value of X? Hint: This is a problem involving the exponential distribution. Knowing the parameter for the distribution allows you to easily answer parts a,b,c and use the built-in R functions for the exponential distribution (dexp(), pexp(), gexp()) for other parts. Or (not recommended) you should be able to use the R integrate command with f(x) defined as above or with dexp() for all parts. b) What is the variance of X? c) What is the standard deviation of X? is what R calls rate. d) What is the probability that X is larger than its expected value? e) What is the probability that X is > 5? f) What is the probability that X is > 10? . Thus, the density of X is: g) What is the probability that X > 10 given that X > 5? h) What is the median of X?The formula used to calculate a confidence interval for the mean of a normal population when n is small is the following. xt (t critical value) √n What is the appropriate t critical value for each of the following confidence levels and sample sizes? (Round your answers to two decimal places.) USE SALT (a) 98% confidence, n = 17 (b) 90% confidence, n = 12 (c) 98% confidence, n = 24 (d) 90% confidence, n = 25 (e) 80% confidence, n = 13 (f) 95% confidence, n = 10Stoaches are fictional creatures, sometimes mistaken for mome raths. Suppose a two-tailed t-test is conducted to test for a difference between the population means of adult female stoach weights and adult male stoach weights. The female sample has 13 weights, and the male sample has 7 weights. The t-statistic for the test is -0.20542. What is the p-value? (Give your answer to 4 decimal places.) p-value:
- How would you report the results? The derived t = 0.02 was not significant at p = .05 with df = 10. Therefore, Ho was not rejected, and it was concluded that the mean pretest score for students at the beginning of the semester (18.27) was not different than the mean posttest score for students at the end of the semester (22.00), t(10) -= 0.02, p .05. In terms of the research question, it appears that the curriculum was not effective in promoting learning.Can you help me with this please! Thank you.