You are trying to estimate the average height of people living in New York. You have...
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You are trying to estimate the average height of people living in New York. You have two people who are helping you, by measuring the heights of randomly chosen people. John, the first person helping you measures the height of 10 people. Susan, the second person helping you also measures the heights of 10 people. It turns out that John is a troublemaker and is trying to sabotage your study by adding a randomly chosen number to each person he measures' height. So for example, the height of the first person John reports to you is J₁ = H₁ + R₂ Where H1 is the true height of the first person John measures, R₁ is a random number John adds to H₁1, and Ji is the number that John reports to you as the height of the first person he measures. The second height that John reports to you would also be incorrect because he would add a random variable to it: J₂ = H₂2+R₂ Susan, on the other hand is just trying to be helpful, not screw up your study, so she simply reports the heights as she measures them: S₁ = H₂₁ Where H, is the true height of the first person she measures, and S₁ is the height she measures. Assume the following to be true • E[R] = 0 • Var(H) = Var (R₂) = Var (H₂) • Var(J)=2x Var(S₁) (a) You are trying to estimate the average height of the population, #, which is equal to E[H₁₁] and E[H.]. If you added up the ten heights reported by John and the ten heights reported by Susan and then divided by 20, would that be an unbiased estimator of ? In other words, is the expected value of the estimator below equal to u? Σ+Σ, S 20 10 You are trying to estimate the average height of people living in New York. You have two people who are helping you, by measuring the heights of randomly chosen people. John, the first person helping you measures the height of 10 people. Susan, the second person helping you also measures the heights of 10 people. It turns out that John is a troublemaker and is trying to sabotage your study by adding a randomly chosen number to each person he measures' height. So for example, the height of the first person John reports to you is J₁ = H₁ + R₂ Where H1 is the true height of the first person John measures, R₁ is a random number John adds to H₁1, and Ji is the number that John reports to you as the height of the first person he measures. The second height that John reports to you would also be incorrect because he would add a random variable to it: J₂ = H₂2+R₂ Susan, on the other hand is just trying to be helpful, not screw up your study, so she simply reports the heights as she measures them: S₁ = H₂₁ Where H, is the true height of the first person she measures, and S₁ is the height she measures. Assume the following to be true • E[R] = 0 • Var(H) = Var (R₂) = Var (H₂) • Var(J)=2x Var(S₁) (a) You are trying to estimate the average height of the population, #, which is equal to E[H₁₁] and E[H.]. If you added up the ten heights reported by John and the ten heights reported by Susan and then divided by 20, would that be an unbiased estimator of ? In other words, is the expected value of the estimator below equal to u? Σ+Σ, S 20 10
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Data Analysis and Decision Making
ISBN: 978-0538476126
4th edition
Authors: Christian Albright, Wayne Winston, Christopher Zappe
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