i) Derive the standard error of 3, se() = 0.0009, using MLE approach. ii) Find an approximate 95% Confidence interval for B.
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Firstly it is required to determine the MLE of the parameter and then the variance to get the required confidence interval.
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- Find the 95% confidence interval for estimating the population mean μ If sample mean X = 50, sample size n= 60 and population standard deviation σ is known to be 10.The 82.9% confidence interval estimate for μμ was (25.81, 31.35). Find the point estimate and the margin of error (ME) from this interval estimate. Point estimate = ME=A random sample of 25 students obtained a mean of 78 and a variance of s2 = 15 on a college entrance exam in engineering. Assuming the scores are normally distributed, construct a 98% confidence interval of σ2
- Use the t-distribution to find a confidence interval for a difference in means μ1−μ2μ1-μ2 given the relevant sample results. Give the best estimate for μ1−μ2μ1-μ2, the margin of error, and the confidence interval. Assume the results come from random samples from populations that are approximately normally distributed.A 95% confidence interval for μ1−μ2μ1-μ2 using the sample results x⎯⎯1=515x¯1=515, s1=136s1=136, n1=300n1=300 and x⎯⎯2=462x¯2=462, s2=94s2=94, n2=200n2=200Enter the exact answer for the best estimate and round your answers for the margin of error and the confidence interval to two decimal places.Best estimate = Enter your answer; Best estimateMargin of error = Enter your answer; Margin of errorConfidence interval : Enter your answer; Confidence interval, value 1 to Enter your answer; Confidence interval, value 2IF n < 30 AND T= Y- SHOW HOW THE 100(1-2a)% CONFIDENCE INTERVAL FOR μL IS DERIVED 5/√T²A new method has been developed in the treatment of a disease. 12 randomly selected patients were treated with this method and the time until recovery was calculated as in the picture. Establish a confidence interval for the mass mean µ. (α=0.05)
- Let X equal the length of life of a 60-watt light bulb marketed by a certain manufacturer. We do not know the distribution of X except that Var(X) = 1158. Let u be the mean of X. Suppose a random sample of n = 25 bulbs is tested until they burn out, yielding a sample mean of = 1368 hours. (i) Compute an approximate 95% confidence interval for u. (ii) Compute an approximate 95% one-sided confidence interval for that provides a lower bound for u, i.e. compute & such that ɛ P(X - ≤ μµ)≈ 0.95.Why should a confidence interval for p fall between (0, 1) while it makes sense for a confidence interval for Pi - p2 to fall between (-1, 1)?Suppose a marketing company randomly surveyed 404 households and found that in 214 of them, the woman made the majority of the purchasing decisions. Construct a 90% confidence interval for the population proportion of households where the women make the majority of the purchasing decisions.p'=α2=zα2=Margin of Error: E=We are 90% confident that the proportion of households in the population where women make the majority of purchasing decisions is between___ and ___.
- Let X1, X2, X3, ..., X, be a random sample from a distribution with known variance Var(X,) = o², and unknown mean EX, = 0. Find a (1 – a) confidence interval for 0. Assume that n is large.6.05 Based on a random sample of size n = 40, the 95% confidence interval for the true mean weight in mg for beans of a certain type is (229.7,233.5). Obtain the 99% confidence interval.Use a t-distribution to find a confidence interval for the difference in means μ = μ₁ −μ₂ using the relevant sample results from paired data. Assume the results come from random samples from populations that are approximately normally distributed, and that differences are computed using d = x₁ - x₂. A 95% confidence interval for µå using the paired difference sample results ād Give the best estimate for μd, the margin of error, and the confidence interval. Enter the exact answer for the best estimate, and round your answers for the margin of error and the confidence interval to two decimal places. Best estimate = Margin of error: = The 95% confidence interval is i to i = : 3.1, Sa = : 2.3, na = 30.
