Question

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In Lesson Eight you've learned how to construct confidence intervals for population parameters and proportions, based on data from samples.

1. In a short paragraph, distinguish between Sampling Error and the Margin of Error. Explain what each represents and the relationship between them.
2. In a short paragraph, distinguish between a Point Estimate and an Interval Estimate. Explain what each represents and the relationship between them.
3. In a short paragraph, distinguish between a Confidence Interval and the Level of Confidence. Explain what each represents and the relationship between them.
4. Identify the three components of a Confidence Interval. Explain what each represents and the relationship between them.
5. Describe a potential issue with public opinion polls that report interval estimates, but not confidence intervals. Discuss this in a short paragraph.

Answer 1

(a)

Sampling Error is a statistical error that occurs when an analyst does not select a sample that represents the entire population of data. The Margin of Error for a statistic is an interval estimate: a pair of percentages surrounding a guess about an attribute of full population based on a random sample from that population.

Relationship between Sampling Error and Margin of Error: Margin of Error is an interval that is used to give an indication of the amount of uncertainty due to Sampling Error when using data from a Random Sample to estimate a population parameter.

(b)

The Point Estimate of a population parameter is a single value that is used to estimate the population parameter, Interval estimate is defined by two numbers between which a population parameter is said to lie.

Relationship between Point Estimate and Interval Estimate: The interval estimate consists of a range of values and has the advantage of providing greater confidence than a point estimate.

(c)

Confidence Interval (CI) is a type of interval estimate,computed from the statistic of the observed data, that contains the true value of the unknown population parameter. Level of Confidence refers to the percentage of all possible samples that can be expected to include the true population parameter.

Relationship between Confidence Interval and Level of Confidence: Confidence Level defines the distance for how close the Confidence Limits are to sample mean.

(d)

Three components of a Confidence Interval:
(i) Confidence level

(ii) statistic

(iii) Margin of Error

The Confidence Level describes the uncertainty of a sampling method. The statistic and the margin of error define an interval estimate that describes the precision of the method.

Relationship between them:

The interval estimate of a Confidence Interval is defined by the sample statistic Margin of Error.

(e)

Many public opinion surveys report interval estimates, but ot confidence intervals. They provide the margin of error, but not the Confidence Level. To clearly interpret thesurvey, we need toknow both.