Asked by Gracio
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A measurement follows the normal distribution with a standard deviation of 15 and an unknown expectation μ. You can consider that measurement to be the "original" distribution. Two statisticians propose two distinct ways to estimate the unknown quantity μ with the aid of a sample of size 36. They will do that by evaluating two different SAMPLING DISTRIBUTIONS to determine which method is better. There are two statisticians involved in this task: statistician "A" and statistician "B." Statistician A proposes to use the sampling distribution of the sample average as an estimate. Statistician B proposes to use the sampling distribution of the sample median instead. In order to choose between the two options they agree to prefer the statistic that has a smaller variance (with respect to the sampling distribution). Tasks 1-9 refer to this problem of comparing the two statistics to each other.
1. Assume that the actual expectation of the measurement is equal to 5 (μ=5). Then the expectation of the statistic that was proposed by Statistician A is equal to: ____________
2. Assume that the actual expectation of the measurement is equal to 5 (μ=5). Then the standard deviation of the statistic that was proposed by Statistician A is equal to: _______
3. Assume that the actual expectation of the measurement is equal to 5 (μ=5). Then the expectation of the statistic that was proposed by Statistician B is equal to: ________Select one: a. 2.3 b. 3.7 c. 4.1 d. 5.0
4. Assume that the actual expectation of the measurement is equal to 5 (μ=5). Then the standard deviation of the statistic that was proposed by Statistician B is equal to: Select one: a. 2.0 b. 2.5 c. 3.0 d. 3.5
5. Assume that the actual expectation of the measurement is equal to 2.3 (μ=2.3). Then the expectation of the statistic that was proposed by Statistician A is equal to: ______
6. Assume that the actual expectation of the measurement is equal to 2.3 (μ=2.3). Then the standard deviation of the statistic that was proposed by Statistician A is equal to: Answer: ________
7. Assume that the actual expectation of the measurement is equal to 2.3 (μ=2.3). Then the expectation of the statistic that was proposed by Statistician B is equal to: Select one: a. 2.3 b. 3.7 c. 4.1 d. 5.0
8. Assume that the actual expectation of the measurement is equal to 2.3 (μ=2.3). Then the standard deviation of the statistic that was proposed by Statistician B is equal to: Select one: a. 2.0 b. 2.5 c. 3.0 d. 3.5
9. Based on the information collected in Tasks 1-8, which of the two statistics produces values which tends to be more concentrated about the expectation of the measurement? Select one:
a. The statistic proposed by Statistician A
b. The statistic proposed by Statistician B
A measurement follows the normal distribution with a standard deviation of 15 and an unknown expectation μ. You can consider that measurement to be the "original" distribution. Two statisticians propose two distinct ways to estimate the unknown quantity μ with the aid of a sample of size 36. They will do that by evaluating two different SAMPLING DISTRIBUTIONS to determine which method is better. There are two statisticians involved in this task: statistician "A" and statistician "B." Statistician A proposes to use the sampling distribution of the sample average as an estimate. Statistician B proposes to use the sampling distribution of the sample median instead. In order to choose between the two options they agree to prefer the statistic that has a smaller variance (with respect to the sampling distribution). Tasks 1-9 refer to this problem of comparing the two statistics to each other.
1. Assume that the actual expectation of the measurement is equal to 5 (μ=5). Then the expectation of the statistic that was proposed by Statistician A is equal to: ____________
2. Assume that the actual expectation of the measurement is equal to 5 (μ=5). Then the standard deviation of the statistic that was proposed by Statistician A is equal to: _______
3. Assume that the actual expectation of the measurement is equal to 5 (μ=5). Then the expectation of the statistic that was proposed by Statistician B is equal to: ________Select one: a. 2.3 b. 3.7 c. 4.1 d. 5.0
4. Assume that the actual expectation of the measurement is equal to 5 (μ=5). Then the standard deviation of the statistic that was proposed by Statistician B is equal to: Select one: a. 2.0 b. 2.5 c. 3.0 d. 3.5
5. Assume that the actual expectation of the measurement is equal to 2.3 (μ=2.3). Then the expectation of the statistic that was proposed by Statistician A is equal to: ______
6. Assume that the actual expectation of the measurement is equal to 2.3 (μ=2.3). Then the standard deviation of the statistic that was proposed by Statistician A is equal to: Answer: ________
7. Assume that the actual expectation of the measurement is equal to 2.3 (μ=2.3). Then the expectation of the statistic that was proposed by Statistician B is equal to: Select one: a. 2.3 b. 3.7 c. 4.1 d. 5.0
8. Assume that the actual expectation of the measurement is equal to 2.3 (μ=2.3). Then the standard deviation of the statistic that was proposed by Statistician B is equal to: Select one: a. 2.0 b. 2.5 c. 3.0 d. 3.5
9. Based on the information collected in Tasks 1-8, which of the two statistics produces values which tends to be more concentrated about the expectation of the measurement? Select one:
a. The statistic proposed by Statistician A
b. The statistic proposed by Statistician B
Answers
Answered by
John Smith
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