A. In a short paragraph, distinguish between Sampling Error and the Margin of Er

Question

A. In a short paragraph, distinguish between Sampling Error and the Margin of Error. Explain what each represents and the relationship between them.

B. In a short paragraph, distinguish between a Point Estimate and an Interval Estimate. Explain what each represents and the relationship between them.

C. In a short paragraph, distinguish between a Confidence Interval and the Level of Confidence. Explain what each represents and the relationship between them.

D. Identify the three components of a Confidence Interval. Explain what each represents and the relationship between them.

E. What is the problem with public opinion polls that report interval estimates, but not confidence intervals? Discuss this in a short paragraph.

Explanation / Answer

A)

Sampling errors occur because only a sample of the population is investigated. The particular sample used in this survey is one of a large number of possible samples of the same size that could have been selected using the same sampling method. It is clear that estimates based on different samples will differ from one another,and almost all of them will differ from the value obtained had a complete census been taken – “the census value”

The margin of error expresses the maximum expected difference between the true population parameter and a sample estimate of that parameter. To be meaningful, the margin of error should be qualified by a probability statement (often expressed in the form of a confidence level).

B)

https://www2.stat.duke.edu/courses/Spring02/sta103/lec/ch8b_4.pdf

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C)

A confidence level refers to the percentage of all possible samples that can be expected to include the true population parameter. For example, suppose all possible samples were selected from the same population, and a confidence interval were computed for each sample. A 95% confidence level implies that 95% of the confidence intervals would include the true population parameter.

Confidence interval is always in the same unit as the population parameter or sample statistic. Confidence interval is generated/calculated using the confidence level required by the user with the help of z table/t table/chi-square table based on the distribution.

D)

To express a confidence interval, you need three pieces of information.

         Margin of error = Critical value * Standard deviation of statistic

            Confidence interval = sample statistic + Margin of error

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