statistics
What is stratified sampling?
Obtain the unbiased estimator of population total. Obtain the variance of the estimator.
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1. Select all true statements about sample mean and sample median. A) When the population distribution...
1. Select all true statements about sample mean and sample median. A) When the population distribution is skewed, sample mean is biased but sample median is an unbiased estimator of population mean. B) When the population distribution is symmetric, both mean and sample median are unbiased estimators of population mean. C) Sampling distribution of sample mean has a smaller standard error than sample median when population distribution is normal. D) Both mean and median are unbiased estimators of population mean...
3. You have two independent random samples: XiXX from a population with mean In and variance σ2 a...
3. You have two independent random samples: XiXX from a population with mean In and variance σ2 and Y, Y2, , , , , Y,n from a population with mean μ2 and variance σ2. Note that the two populations share a common variance. The two sample variances are Si for the first sample and Si for the second. We know that each of these is an unbiased estimator of the common population variance σ2, we also know that both of...
10.2 For the sample in problem 10.1, consider another estimator of u (call it ê) that...
10.2 For the sample in problem 10.1, consider another estimator of u (call it ê) that is defined as follows: ( 10.1 Suppose that we have a simple random sample of size 3 from a population with mean w. Our estimator of u is ê, defined as follows: When sampling from a nonnormal population, there may be unbiased es- timators of u that are more efficient than X. These estimators, however, would be nonlinear functions of the Xi's; that is,...
Quiz: Module 2 Quiz This Question: 1 pt 9 of 10 (8 complete) Consider the population...
Quiz: Module 2 Quiz This Question: 1 pt 9 of 10 (8 complete) Consider the population described by the probability distribution shown in the table. The random variable x is observed twice. If these observations are independen probabilities are shown in the accompanying table Complete parts a through e below. DI! Click the icon to view the table. Find the sampling distribution of s? Type the answers in ascending order fors? HP P( 0.22 0.32 0.24 Type integers or decimals.)...
CLUSTER SAMPLING WITH ESTIMATION Suppose a population of size N is divided into K- N/M groups of size M. We select a sample of size n -km the following way: » First we select k groups out of K groups...
CLUSTER SAMPLING WITH ESTIMATION Suppose a population of size N is divided into K- N/M groups of size M. We select a sample of size n -km the following way: » First we select k groups out of K groups by simple random sampling . We then select m units in each group selected on the first step by simple random sampling . The estimate of the population mean is the average Y of the sample. Let μί be the...
If X, X2,..., Xn constitute a random sample from the population with pdf ffx) 0 elsewhere...
If X, X2,..., Xn constitute a random sample from the population with pdf ffx) 0 elsewhere a) ind the E(X) and hence show that X is a biased estimator of 0. What is the bias? b)What estimator based on X would be an unbiased estimator of 0? Why? nen( y1-0) y, > c Given g(y,)- show that Yı= min ( X1, X2, Х. ) is a consistent 0 otherwise estimator of the parameter 0 d) Obtain the mean of Y,....
1. With random sampling, there is homogeneity within a subgroup or stratum. What type of random...
1. With random sampling, there is homogeneity within a subgroup or stratum. What type of random sampling method was chosen? Select one: a. stratified sampling b. systematic sampling c. convenience sampling d. simple random sampling 2. A property of a point estimator that occurs whenever the expected value of the point estimator is equal to the population parameter it estimates is known as Select one: A. consistency B. the expected value C. the estimator D. unbiasedness
statistics
Let T1 and T2 be two independent unbiased estimators for with var(T1) = 2 var(T2). Find theconstants k1 and k2 so that k1 T1 + k2 T2 is an unbiased estimator for with smallest variance forsuch a linear combination
statistics
Suppose X , X ,..., X n 1 2 be a random sample drawn from a population with mean θand varianceσ2 . Show that Ti=1/i∑Xj is unbiased estimator of θ (i = 1,2,…,n). Also show var(Ti ) is monotonically decreasing. Hence find the best unbiased estimator for θ.
A survey was undertaken to estimate the hours worked per week by volunteers in a social...
A survey was undertaken to estimate the hours worked per week by volunteers in a social service agency. The agency provides telephone support 7 days a week for 12 hours each day. There are currently 12,478 volunteers across the country. This number is the number recorded in the volunteer register on 1 May 2018. 100 of these volunteers were randomly chosen. The 100 were each sent an email and asked to record the total hours they worked for the week...
3. You have two independent random samples: XiXX from a population with mean In and variance σ2 and Y, Y2, , , , , Y,n from a population with mean μ2 and variance σ2. Note that the two populations share a common variance. The two sample variances are Si for the first sample and Si for the second. We know that each of these is an unbiased estimator of the common population variance σ2, we also know that both of...
10.2 For the sample in problem 10.1, consider another estimator of u (call it ê) that is defined as follows: ( 10.1 Suppose that we have a simple random sample of size 3 from a population with mean w. Our estimator of u is ê, defined as follows: When sampling from a nonnormal population, there may be unbiased es- timators of u that are more efficient than X. These estimators, however, would be nonlinear functions of the Xi's; that is,...
Quiz: Module 2 Quiz This Question: 1 pt 9 of 10 (8 complete) Consider the population described by the probability distribution shown in the table. The random variable x is observed twice. If these observations are independen probabilities are shown in the accompanying table Complete parts a through e below. DI! Click the icon to view the table. Find the sampling distribution of s? Type the answers in ascending order fors? HP P( 0.22 0.32 0.24 Type integers or decimals.)...
CLUSTER SAMPLING WITH ESTIMATION Suppose a population of size N is divided into K- N/M groups of size M. We select a sample of size n -km the following way: » First we select k groups out of K groups by simple random sampling . We then select m units in each group selected on the first step by simple random sampling . The estimate of the population mean is the average Y of the sample. Let μί be the...
If X, X2,..., Xn constitute a random sample from the population with pdf ffx) 0 elsewhere a) ind the E(X) and hence show that X is a biased estimator of 0. What is the bias? b)What estimator based on X would be an unbiased estimator of 0? Why? nen( y1-0) y, > c Given g(y,)- show that Yı= min ( X1, X2, Х. ) is a consistent 0 otherwise estimator of the parameter 0 d) Obtain the mean of Y,....
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