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1. Assume there are a population size N = 6 with units (2,4,6,8, 10, 12), and out of which sample size n = 5 units are to be selected based on simple random sampling without replacement. a. Prove that the mean of the sample is unbiased estimator for the population mean. b. Find the mean and variance of the random variable Y = (X/) + 10, where si = (x, - 1)* is unbiased estimator of the variance of the random sample X to the population variance, and X is the population mean. 2. Prove that the simple random sampling without replacement is more efficient than simple random sampling with replacement.

1. Assume there are a population size N = 6 with units (2,4,6,8, 10, 12), and out of which sample size n = 5 units are to be selected based on simple random sampling without replacement. a. Prove that the mean of the sample is unbiased estimator for the population mean. b. Find the mean and variance of the random variable Y = (X/) + 10, where si = (x, - 1)* is unbiased estimator of the variance of the random sample X to the population variance, and X is the population mean. 2. Prove that the simple random sampling without replacement is more efficient than simple random sampling with replacement.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.4: Distributions Of Data
Problem 19PFA
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Q3: Answer the following: 1. Assume there are a population size N = 6 with units (2, 4, 6,8, 10, 12), and out of which sample size n = 5 units are to be selected based on simple random sampling without replacement. a. Prove that the mean of the sample is unbiased estimator for the population mean. b. Find the mean and variance of the random variable Y = (*/) + 10, where si =E(x- )² is unbiased estimator of the variance of the random sample X to the population variance, and is the population mean. 2. Prove that the simple random sampling without replacement is more efficient than simple random sampling with replacement.
Transcribed Image Text:Q3: Answer the following: 1. Assume there are a population size N = 6 with units (2, 4, 6,8, 10, 12), and out of which sample size n = 5 units are to be selected based on simple random sampling without replacement. a. Prove that the mean of the sample is unbiased estimator for the population mean. b. Find the mean and variance of the random variable Y = (*/) + 10, where si =E(x- )² is unbiased estimator of the variance of the random sample X to the population variance, and is the population mean. 2. Prove that the simple random sampling without replacement is more efficient than simple random sampling with replacement.
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