LX2 For a random sample of size n For a random sample ofsice n ta). Show...
Suppose that Y1 , Y2 ,..., Yn denote a random sample of size n from a normal population with mean μ and variance 2 . Problem # 2: Suppose that Y , Y,,...,Y, denote a random sample of size n from a normal population with mean u and variance o . Then it can be shown that (n-1)S2 p_has a chi-square distribution with (n-1) degrees of freedom. o2 a. Show that S2 is an unbiased estimator of o. b....
10. A simple random sample of size n is drawn. The sample mean x is found to be 39.1, and the sample standard deviation s is found to be 9.7. a) (2 points) Construct a 90% confidence interval for the population mean u if the sample size n is 41. b) (2 points) Construct a 90% confidence interval for the population mean y if the sample size n is 101. c) (2 points) Construct a 99% confidence interval for the...
suppose a simple random sample size n=49 Suppose a simple random sample of size n= 49 is obtained from a population with u = 82 and o = 28. (a) Describe the sampling distribution of x. (b) What is P (X> 86.2)? (c) What is P (572) (d) What is P (76<x< 88.6)? Click here to view the standard normal distribution table page) Click here to view the standard normal distribution table (page 2). (a) Choose the correct description of...
n be a random sample from a Gamma distribution with (a) Show there exists a uniformly most powerful test for testing Ho vs H. Show that the critical region can be expressed as an inequality for Y-:-1X, that is it will have the form [Y>cor the form Y < c]. Explain which one of the two and why (b) Is there a uniformly most powerful test for testing Ho : θ 1 vs H1 : θメ1? axqplai n be a...
6.1.29 ge Find the minimum sample size n needed to estimate u for the given values of c, a, and E c 0.98, o 5.4, and E 2 Assume that a preliminary sample has at least 30 members (Round up to the nearest whole number.) n= rked Scon ts: mewi estion estion hat to Enter your answer in the answer box and then click Check Answer rse (SUM All parts showing Use Prid Cear A DELL
1. A sample size of n-20 is a simple random sample selected from a normally distributed population. Find the critical value ta2 corresponding to a 95% confidence level. 2.093 O 2.086 02.861 1.960 2. Assume you want to construct a 90% confidence interval from sample of a distributed population. The sample size is 37. Find the critical value to2 1.687 2.719 1.688 O1.645 3. You are constructing a 95% confidence interval of a sample space consisting of n = 40...
Question: Let Y, Y be a random sample of size n=2 from a distribution with Pdf f(y; 6) = (6)e-0 OLGLD and o elsewhere We reject Ho : O=2 and accept H1:0=1 if the observed values of Y la are such that: fu, ; 2) fűz; 2) at f(4,;1) fŲz;1) 1 * Find the Significance level and the Power of the test when Ho is falso; given that {0:0=1,2}.
Problem 8.2 Suppose that Xi, X,.., Xn is a random sample of size n is to be taken from a population with pdf 2 In>X (In2) x We are interested in determining the approximate distribution of the sample geometric mean given by [x. If we let Y-In X, then we can re-express the geometric mean as a) Determine the mean of Y. Hint, if u = In x, then du = 1/x dx. b) Determine the variance of Y. c)...
10. A simple random sample of size n is drawn. The sample mean x is found to be 39.1, and the sample standard deviation s is found to be 9.7. a) (2 points) Construct a 90% confidence interval for the population mean w if the sample size n is 41. b) (2 points) Construct a 90% confidence interval for the population mean 4 if the sample size n is 101. c) (2 points) Construct a 99% confidence interval for the...
A simple random sample of size n is drawn. The sample mean, x, is found to be 19.4, and the sample standard deviation, s, is found to be 4.9. Click the icon to view the table of areas under the t-distribution. (a) Construct a 95% confidence interval about if the sample size, n, is 35. Lower bound: :Upper bound: (Use ascending order. Round to two decimal places as needed.) (b) Construct a 95% confidence interval about if the sample size,...