Suppose we are trying to measure some physical constant . Assume that each time w easure µ, there is a small, independent random error ~ N(0, 0²) with o = 0.01. (i) How many measurements do we need to construct a 99% confidence interval of lengt 0.01 for u? (ii) If we can only afford to make only 10 measurements, what level of confidence can w achieve for a confidence interval of length 0.01?
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- Heights (cm) and weights (kg) are measured for 100 randomly selected adult males, and range from heights of 130 to 192 cm and weights of 38 to 150 kg. Let the predictor variable x be the first variable given. The 100 paired measurements yield x 167.67 cm. y=81.53 kg. r=0.356, P-value=0.000, and y= -106 +1.14x. Find the best predicted value ofy (weight) given an adult male who is 177 cm tall. Use a 0.05 significance level. The best predicted value of y for an adult male who is 177 cm tall is kg. (Round to two decimal places as needed.)he personality trait of "Conscientiousness" (someone who is organized, responsible, and can control their impulses) has μ = 120 and σ =9. Test whether ARC students (n = 9, M = 126) differ on Conscientiousness. α = .05. What is the correct result based on the data?Ex X is a Gaussian random variable with E(x)= 0 and P[IXIF10] =01. what is the standred deviation 3 ?
- A psychologist developed a standardized test for selecting “gifted” children. In the population, the test scores are normally distributed, with μ=75μ=75 and σ=10σ=10. We randomly sampled 49 gifted students and found out the mean test score of these 49 students is 77. Over repeated samples (with a fixed n=49n=49), what is the probability of getting a sample mean that is equal to or greater than the one we got? A. 0.42074 B. 0.91924 C. 0 D. 0.57925 E. 0.08076The scores of a random sample of 100 high school students on a standardized mathematics test in a certain school gave a mean of 78 and a standard deviation of 20.Find the 95% confidence interval estimate for the true average score in mathematics in this standardized test. Formula: E=zα/2(σ/√n)A certain model of car can be ordered with either a large or small engine. The mean number of miles per gallon for cars with a small engine is 6.8. An automotive engineer thinks that the mean for cars with the larger engine is higher than this. State the appropriate null and alternate hypotheses. The null hypothesis is Hoμ (Choose one) The alternate hypothesis is H₁ μu (Choose one) ×
- Now, suppose you run an Auto Arima and you find R gives you the following model: Identify the ARIMA (p,d,q) i.e how many p terms are there? How many q terms? Coefficients: ar1 ma1 ma2 -0.7921 -0.0970 -0.3945 s.e. 0.1396 0.1802 0.1580 sigma^2 estimated as 0.1834: log likelihood=-44.07 AIC=96.14 AICc=96.68 BIC=105.61Let X₁, ..., X be a random sample from a gamma distribution with a x = 2 and 3 = = 0. '1' 1. Find the simplified likelihood of 0 given x: L(01x). 2. Find the maximum likelihood estimator of 0,0 MLE* is unbiased. 3. Show that the value you found for 0 MLE2. If x is a value assumed by a random variable X having the exponential distribution given by x > 0, elsewhere f(x)= = 0 >0 Ө 0, Find k so that the interval 0 <0The mean and standard deviation of a random variable are 11 and 1 respectively. Find the mean and standard deviation of the given random variables: (1) y = x + 6 H = o = (2) v = 3x H = σ = (3) w = 3x + 6 fb= J =Answer parts a and b of the following question. Show work. Let Y > 0 be a continuous random variable representing time from regimen start to bone-marrow transplant. Everyone does not survive long enough to get the transplant. Let X > 0 be a continuous random variable representing time from regimen start to death. We can assume X ⊥ Y and model time to death as X ∼ Exp(rate = θ) and time to transplant as Y ∼ Exp(rate = µ). Where Exp(rate = λ) denotes the exponential distribution with density f(z | λ) = λe−λz for z > 0 and 0 elsewhere - with λ > 0. a.) Compute the probability that a patient dies before receiving transplant. b.) Assume that we have θ = 1/10 and µ = 1/15. Use the rexp() function in R for i = 1, 2, . . . , 10000 in simulating death and transplant times for 10,000 patients Xi ∼ Exp(1/10) and Yi ∼ Exp(1/15). What is the proportion of simulated patients who receive transplant before death?Answer parts a and b of the following question. Show work. Let Y > 0 be a continuous random variable representing time from regimen start to bone-marrow transplant. Everyone does not survive long enough to get the transplant. Let X > 0 be a continuous random variable representing time from regimen start to death. We can assume X ⊥ Y and model time to death as X ∼ Exp(rate = θ) and time to transplant as Y ∼ Exp(rate = µ). Where Exp(rate = λ) denotes the exponential distribution with density f(z | λ) = λe−λz for z > 0 and 0 elsewhere - with λ > 0. a.) In probability/random variable notation, express the probability that a patient receives transplant before death b.) For this problem, what is the joint density fXY (x, y)? Show that it is a valid density.SEE MORE QUESTIONS