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Below are the values for two variables x and y obtained from a sample of size...
QUESTION 5 Suppose you obtained one sample from the same data generating process as above (Y...
QUESTION 5 Suppose you obtained one sample from the same data generating process as above (Y = 2 + 3x+ u), and your estimate β 1 (the estimated X coefficient) was 2.107. Which of the following best describes whether the estimator is biased? The estimator is biased because the estimate 2.107 is too far below the population parameter of 3 The estimator is not biased because the estimate 2.107 is within 30 percent of the population parameter 3. We do...
A random sample of size 15 is obtained from a normal population yielding a sample standard...
A random sample of size 15 is obtained from a normal population yielding a sample standard deviation of 20. Test the null hypothesis that the unknown population variance is greater than or equal to 162 versus the alternative that the unknown population variance is less than 162 using a 5% level of significance a. Set up the null and alternative hypotheses, clearly defining any unknown parameters. Note the “=” value is always in the null hypothesis. b. Find a test...
7. You are testing the null hypothesis that there is no linear relationship between two variables,...
7. You are testing the null hypothesis that there is no linear relationship between two variables, X and Y. From your sample of n=18, you determine that b1=4.4 and Sb1=1.7. a. What is the value of tSTAT? b. At the α=0.05 level of significance, what are the critical values? c. Based on your answers to (a) and (b), what statistical decision should you make? d. Construct a 95% confidence interval estimate of the population slope, β1. 8. You are testing...
A random sample of size n= 15 obtained from a population that is normally distributed results...
A random sample of size n= 15 obtained from a population that is normally distributed results in a sample mean of 45.8 and sample standard deviation 12.2. An independent sample of size n = 20 obtained from a population that is normally distributed results in a sample mean of 51.9 and sample standard deviation 14.6. Does this constitute sufficient evidence to conclude that the population means differ at the a = 0.05 level of significance? Click here to view the...
A random sample of size n = 13 obtained from a population that is normally distributed...
A random sample of size n = 13 obtained from a population that is normally distributed results in a sample mean of 45.2 and sample standard deviation 12.6. An independent sample of size n=17 obtained from a population that is normally distributed results in a sample mean of 51.1 and sample standard deviation 14.9. Does this constitute sufficient evidence to conclude that the population means differ at the a= 0.10 level of significance? Click here to view the standard normal...
the unknown Popular random sample of size 17 is obtained from a normal (15) 4.Malding a...
the unknown Popular random sample of size 17 is obtained from a normal (15) 4.Malding a sample standard deviation of S. Teet the nuit that the unknown population variance is greater than or 169, versus the alternative hypothesis that the unknown lance is less than 169 using a 1% level of significance hypothesis that Set up the null and alternative hypotheses, clearly defining any unknown parameters. Note the value is always in the mull hypothesis m atatest statistie: (1) sensitive...
Let ρ represent the true population coefficient of correlation of two variables X and Y ....
Let ρ represent the true population coefficient of correlation of two variables X and Y . Suppose you want to test the hypothesis that ρ = 0. Explain how you would test this hypothesis. [Hint: by the relationship between b1 and rXY ]
Consider the following point estimators, W, X, Y, and Z of μ: W = (x1 +...
Consider the following point estimators, W, X, Y, and Z of μ: W = (x1 + x2)/2; X = (2x1 + x2)/3; Y = (x1 + 3x2)/4; and Z = (2x1 + 3x2)/5. Assuming that x1 and x2 have both been drawn independently from a population with mean μ and variance σ2 then which of the following is true...Which of the following point estimators is the most efficient? A. Z B. W C. X D. Y An estimator is unbiased...
A random sample of size 12 is taken from a population, and for each individual in...
A random sample of size 12 is taken from a population, and for each individual in the sample measurements on two variables (X and Y) are obtained. The sample correlation of X and Y is calculated to be r2=0.549081. Carry out a hypothesis test on H0:ρ=0against HA:ρ≠0. If the null hypothesis is true, then the test statistic will follow a t distribution with what degrees of freedom? Number Calculate the value of the test statistic t using the appropriate formula....
Problem 2. (26 points) Two random variables X and Y are jointly normally distributed, with E(X)x,...
Problem 2. (26 points) Two random variables X and Y are jointly normally distributed, with E(X)x, EY) y and co-variance Cov(X,Y) = ơXY. To estimate the population co-variance ơXY, a very simple random sample is drawn from the population. This random sample consists of n pairs of random variables {OG, Yİ), (XyW), , (x,,y,)). Based on the sample, we construct sample co-variance SXY as: Ti-1 2-1 1. (4 points) Show Σ(Xi-X) (Yi-Y) = Σ Xix-n-X-Y. 2. (4 points) Find E(Xi...
QUESTION 5 Suppose you obtained one sample from the same data generating process as above (Y = 2 + 3x+ u), and your estimate β 1 (the estimated X coefficient) was 2.107. Which of the following best describes whether the estimator is biased? The estimator is biased because the estimate 2.107 is too far below the population parameter of 3 The estimator is not biased because the estimate 2.107 is within 30 percent of the population parameter 3. We do...
A random sample of size n= 15 obtained from a population that is normally distributed results in a sample mean of 45.8 and sample standard deviation 12.2. An independent sample of size n = 20 obtained from a population that is normally distributed results in a sample mean of 51.9 and sample standard deviation 14.6. Does this constitute sufficient evidence to conclude that the population means differ at the a = 0.05 level of significance? Click here to view the...
A random sample of size n = 13 obtained from a population that is normally distributed results in a sample mean of 45.2 and sample standard deviation 12.6. An independent sample of size n=17 obtained from a population that is normally distributed results in a sample mean of 51.1 and sample standard deviation 14.9. Does this constitute sufficient evidence to conclude that the population means differ at the a= 0.10 level of significance? Click here to view the standard normal...
the unknown Popular random sample of size 17 is obtained from a normal (15) 4.Malding a sample standard deviation of S. Teet the nuit that the unknown population variance is greater than or 169, versus the alternative hypothesis that the unknown lance is less than 169 using a 1% level of significance hypothesis that Set up the null and alternative hypotheses, clearly defining any unknown parameters. Note the value is always in the mull hypothesis m atatest statistie: (1) sensitive...
Problem 2. (26 points) Two random variables X and Y are jointly normally distributed, with E(X)x, EY) y and co-variance Cov(X,Y) = ơXY. To estimate the population co-variance ơXY, a very simple random sample is drawn from the population. This random sample consists of n pairs of random variables {OG, Yİ), (XyW), , (x,,y,)). Based on the sample, we construct sample co-variance SXY as: Ti-1 2-1 1. (4 points) Show Σ(Xi-X) (Yi-Y) = Σ Xix-n-X-Y. 2. (4 points) Find E(Xi...
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