WRITTEN ASSIGNMENT UNIT 8.
GUARANTEE GRADE ‘A’ 100%
CORRECT ANSWERS
Estimating the Expectation
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.
Question 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:
Answer:
5
Feedback
The correct answer is: 5
Question 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:
Answer:
2.5
Feedback
The correct answer is: 2.5
Question 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: (In order to
answer this question you may need to conduct a simulation, similar to the simulations
,
GUARANTEE GRADE ‘A’ 100%
CORRECT ANSWERS
Estimating the Expectation
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.
Question 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:
Answer:
5
Feedback
The correct answer is: 5
Question 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:
Answer:
2.5
Feedback
The correct answer is: 2.5
Question 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: (In order to
answer this question you may need to conduct a simulation, similar to the simulations
,
