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I. Suppose population 1 has mean μ1 with variance σ2 and population 2 has mean μ2...
Suppose population 1 has mean with variance σ2 and population 2 has mean μ2 with the...
Suppose population 1 has mean with variance σ2 and population 2 has mean μ2 with the same variance σ. Let sỈ and s denote the sample variances from two samples with size ni and n2 from the corresponding populations, respectively. Show that the pooled estimator pooled is an unbiased estimator of σ2
I. Suppose population 1 has mean μί with variance σ2 and population 2 has mean μ2...
I. Suppose population 1 has mean μί with variance σ2 and population 2 has mean μ2 with the same variance σ2. Let s and s denote the sample variances from two samples with size ni and n2 from the corresponding populations, respectively. Show that the pooled estimator 1i+(2-1)si pooled ni + n2 -2 is an unbiased estimator of σ2.
Suppose population l has mean ,11 with variance σ2 and population 2 has mean Ha with...
Suppose population l has mean ,11 with variance σ2 and population 2 has mean Ha with the same variance σ2. Let s' and s denote the sample variances from two samples with size n and n2 from the corresponding populations, respectively. Show that the pooled estimator (m-1)sit (n2-1)d ni t n22 pooled is an unbiased estimator of σ2
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...
x, and S1 are the sample mean and sample variance from a population with mean μ|...
x, and S1 are the sample mean and sample variance from a population with mean μ| and variance ơf. Similarly, X2 and S1 are the sample mean and sample variance from a second population with mean μ and variance σ2. Assume that these two populations are independent, and the sample sizes from each population are n,and n2, respectively. (a) Show that X1-X2 is an unbiased estimator of μ1-μ2. (b) Find the standard error of X, -X. How could you estimate...
I1. Follow the steps below to show that the pooled estimator $p is an unbi- ased...
I1. Follow the steps below to show that the pooled estimator $p is an unbi- ased estimator for the common standard deviation of two independent sam ples Let Yi, Yi2, ..., Yini denote the random sample of size n from the first population with population mean μ| and population variance σ, and let Y21, Y22, ..., Y2na denote an independent random sample of size n2 from the second population with population mean μ2 and population mean ơ3. Sup- pose that...
Having the worst time trying to answer these three questions below. Assume that σ21=σ22=σ2. Calculate the...
Having the worst time trying to answer these three questions below. Assume that σ21=σ22=σ2. Calculate the pooled estimator of σ2 when the first sample gives s21=128 and the second independent sample gives s22= 128, and n1=n2=36. Give your answer to two decimal places , do not round up or down. And .. Two independent random samples have been slected ; 111 observations from population one and 143 observations from population two. From previous experience it is known that the standard...
Consider the following hypothesis test. H0: μ1 − μ2 = 0 Ha: μ1 − μ2 ≠...
Consider the following hypothesis test. H0: μ1 − μ2 = 0 Ha: μ1 − μ2 ≠ 0 The following results are for two independent samples taken from the two populations. Sample 1 Sample 2 n1 = 80 n2 = 70 x1 = 104 x2 = 106 σ1 = 8.4 σ2 = 7.2 (a) What is the value of the test statistic? (Round your answer to two decimal places.) (b) What is the p-value? (Round your answer to four decimal places.)...
Consider the hypothesis test H0: μ1 = μ2 against H1: μ1 > μ2 with known variances...
Consider the hypothesis test H0: μ1 = μ2 against H1: μ1 > μ2 with known variances σ1=10 and σ2=5. Suppose that sample sizes n1=10 and n2=15 and that x-bar1 = 24.5 and x-bar2 = 21.3. Use alpha = .01. Determine the confidence interval. a) =0 b) ≥2.78 c) ≥3.04 d) ≥-4.74
Considering two Gaussian distributions N1~(μ1,σ1^2) and N2~(μ2,σ2^2), we pick two random variables x1 and x2 in...
Considering two Gaussian distributions N1~(μ1,σ1^2) and N2~(μ2,σ2^2), we pick two random variables x1 and x2 in order to compute the sum x3=x1+x2. We want to prove that: a) x3 follows a gaussian distribution b) estimate mean value μ3 and variance σ3^2 c) repeat the above steps for multivariate Gaussian distributions N1~(μ1,Σ1) and N2~(μ2,Σ2)
Suppose population 1 has mean with variance σ2 and population 2 has mean μ2 with the same variance σ. Let sỈ and s denote the sample variances from two samples with size ni and n2 from the corresponding populations, respectively. Show that the pooled estimator pooled is an unbiased estimator of σ2
I. Suppose population 1 has mean μί with variance σ2 and population 2 has mean μ2 with the same variance σ2. Let s and s denote the sample variances from two samples with size ni and n2 from the corresponding populations, respectively. Show that the pooled estimator 1i+(2-1)si pooled ni + n2 -2 is an unbiased estimator of σ2.
Suppose population l has mean ,11 with variance σ2 and population 2 has mean Ha with the same variance σ2. Let s' and s denote the sample variances from two samples with size n and n2 from the corresponding populations, respectively. Show that the pooled estimator (m-1)sit (n2-1)d ni t n22 pooled is an unbiased estimator of σ2
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...
x, and S1 are the sample mean and sample variance from a population with mean μ| and variance ơf. Similarly, X2 and S1 are the sample mean and sample variance from a second population with mean μ and variance σ2. Assume that these two populations are independent, and the sample sizes from each population are n,and n2, respectively. (a) Show that X1-X2 is an unbiased estimator of μ1-μ2. (b) Find the standard error of X, -X. How could you estimate...
I1. Follow the steps below to show that the pooled estimator $p is an unbi- ased estimator for the common standard deviation of two independent sam ples Let Yi, Yi2, ..., Yini denote the random sample of size n from the first population with population mean μ| and population variance σ, and let Y21, Y22, ..., Y2na denote an independent random sample of size n2 from the second population with population mean μ2 and population mean ơ3. Sup- pose that...
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