Derive a large-sample 95% confidence interval for the maximum likelihood estimator of a.
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- When constructing a confidence interval for μ and/or a hypthesis test, how do you decide whether to use the t distribution or the normal distribution? Are there any circumstances when it is acceptable to use either distribution?Determine the t-score for a 95% confidence interval for a population mean from a sample of size 6. t = [three decimal accuracy]A 99% confidence interval guarantees that the true population mean value lies within this confidence range around the measured mean True False
- During the production of boiler plate, test pieces are subjected to a load, and their elongations are measured. In one particular experiment, five tests will be made, at loads (in MPa) of 11, 37, 54, 70, and 93. The least-squares line will be computed to predict elongation from load. Confidence intervals for the mean elongation will be computed for several different loads. Which of the following intervals will be the widest? Which will be the narrowest? a) The 95% confidence interval for the mean elongation under a load of 53 MPa. b) The 95% confidence interval for the mean elongation under a load of 72 MPa. c) The 95% confidence interval for the mean elongation under a load of 35 MPa.In a random sample of 19 people, the mean commute time to work was 33.6 minutes and the standard deviation was 703 minutes. Assume the population is normally distributed and use a t- distribution construct a 80% confidence interval for the population mean u. What is the margin error of u? Interpret the results.A simple random sample of size 23 has mean x̄ = 1.48 and standard deviation s = 1.32. The population is approximately normally distributed. Construct a 99% confidence interval for the population mean
- Work Time Lost due to Accidents At a large company, the Director of Research found that the average work time lost by employees due to accidents was 102 hours per year. She used a random sample of 21 employees. The standard deviation of the sample was 5.4 hours. Estimate the population mean for the number of hours lost due to accidents for the company, using a 99% confidence interval. Assume the variable is normally distributed. Use a graphing calculator and round the answers to the nearest whole number.While the goal of hypothesis is to test a claim (against Ho), the goal of confidence interval estimation is to estimate a parameter. True FalseIf we REJECT the null hypothesis H0: μ=50 at the 0.05 significance level, then the 95% confidence interval for μ will NOT contain the value 50. True False