Question2

12239 11H12Ella: ( 33 Q m Assignment3MAT2377F191v X Assignment-3-... [I] a/anog-la O MAT 2377C Fall 2019 Assignment 3 Deadline : Wednesday : Nov. 13 in class. Total mark:30 Note : Please answer the following questions,. You must give complete details in your solutions and clearly justify your nal answer. 1. Consider the random sample X1,X2,X3,X4 from a population with mean ,u and standard deviation 0. Consider the W. V?\\ b@%\\ [Q \\ 11 =2X1X4, {2 : (5/8)X1+(1/8)X2+(1/8)X3+(1/8)X4 - Wh'd'm't /\\ (a) [2] Are they unbiased estimators of M? (Why ?) 9 I {@'v (b) [2] Which of the two estimators is best for estimating u ? (Why?) VW 61]; [7' a r (QC) 2. A manufacturer of coil springs is interested in implementing a quality control syste tomion process. As part of this quality system, it is decided to record the number of nonconforming coil springs in each production batch of size 50. During 40 days of production, 40 batches. Here are numerical summaries of the data. mean sd n 9. 325 4 . 485804 40 Let X be a random variable representing the number of nonconforming coil springs in a production batch of size 50. Its mean is denoted [u and its standard deviation is a. (a) [1.5] Give a point estimate for [u and a. (b) [1.5] Compute the (estimated) standard error for the estimate of the mean. (c) [1.5] Construct a 95% condence interval for 11. ) (d [1.5] Without computing the 90% condence interval for u, would you expect the length of the interval to be smaller or larger than the 95% condence interval? Explain your answer in a few sentences. 3. Suppose that university facility with the rank of assistant professor earn an average of $74,000 per year with a standard deviation of $6,000. In an attempt to verify this salary level7 a random sample of 60 assistant professor was selected. (a) [2] Describe the sampling distribution of the sample mean X. /u\\ ' 2 LP\" '9 , S 7- 517W