Introduction to Statistic MATH 1280 Assignment UNIT 8 PDF

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Complete Unit 8 Assignment - Introduction to Statistic Math 1280...

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Home My courses MATH 1280 - AY2021-T5 5 August - 11 August Assignment Unit 8

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Started on Monday, 9 August 2021, 6:37 AM State

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Completed on Monday, 9 August 2021, 6:49 AM Time taken 12 mins 19 secs Marks

12.00/12.00

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100.00 out of 100.00

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Information text 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 Correct Mark 1.00 out of 1.00

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Question text 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

Question 2 Correct Mark 1.00 out of 1.00

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Question text 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

Question 3 Correct Mark 1.00 out of 1.00

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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 that are presented in the book. Choose the option closest to the outcome of the simulation.) Select one: a. 2.3 b. 3.7 c. 4.1 d. 5.0

Question 4 Correct Mark 1.00 out of 1.00

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Question text 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: (In order to answer this question you may need to conduct a simulation, similar to the simulations that are presented in the book. Choose the option closest to the outcome of the simulation.) Select one: a. 2.0 b. 2.5 c. 3.0 d. 3.5

Question 5 Correct Mark 1.00 out of 1.00

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Question text 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: Answer:

2.3

Question 6 Correct Mark 1.00 out of 1.00

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Question text 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:

2.5

Question 7 Correct Mark 1.00 out of 1.00

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Question text 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: (In order to answer this question you may need to conduct a simulation, similar to the simulations that are presented in the book. Choose the option closest to the outcome of the simulation.) Select one: a. 2.3 b. 3.7 c. 4.1 d. 5.0

Question 8 Correct Mark 1.00 out of 1.00

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Question text 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: (In order to answer this question you may need to conduct a simulation, similar to the simulations that are presented in the book. Choose the option closest to the outcome of the simulation.) Select one: a. 2.0

b. 2.5 c. 3.0 d. 3.5

Question 9 Correct Mark 1.00 out of 1.00

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Question text 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

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Information text Normal Approximation of the Sampling Distribution of a Sum Suppose that the expected number of phone calls that are handled by a switchboard in each second is 5.35. Assume that the distribution of the number of phone calls per second follows the Poisson distribution. Tasks 10-12 refer to this information.

Question 10 Correct Mark 1.00 out of 1.00

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Question text The number of phone calls that the switchboard is expected to handle in 1 minute is Answer:

321

Question 11 Correct Mark 1.00 out of 1.00

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Question text The 0.80-percentile of the number of calls per minute is (approximately) equal to: (Use the Normal approximation. The answer may be rounded up to 3 decimal places of the actual value.) Answer:

336.0789

Question 12 Correct Mark 1.00 out of 1.00

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Question text The probability that the switchboard will need to handle no more than 300 call in a minute is: (Use the Normal approximation, without a continuity correction. The answer may be rounded up to 3 decimal places of the actual value.)

Answer:

0.1205773...