Question

Please write in BOLD Thanks :)

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

Sampling Error

It is the error which comes into picture due to outcome of taking a sample from a population rather than using the population itself.

Sampling error refers to the part of the difference between population value and estimate ,derived from a sample.This error can be reduced by increasing the size of the sample.

Margin of Error

The margin of error explains the range of values below & above a confidence interval.

If one obtains many unbiased samples of the same size from a defined population, the difference between the sample percent and the true population percent will be within the margin of error, at least 95% of the time.

Point Estimate and an Interval Estimate

Point estimate provide us the specific value as an estimate of population parameter.

Interval Estimate provide us the range of value which has likelihood to contain the population parameter.This range/interval is known as confidence interval.

Confidence Interval and the Level of Confidence:

Confidence interval in Statistics is a type of range estimate for a population parameter based on one or more samples. For instance if we want to estimate the average height of all teenage USA boys aged 15 from a sample of one hundred 15 years old teens.

• The Confidence Level associated to this interval would tell us the percentage of all possible samples that can be expected to include the true population parameter. The usual values are 90%, 95% and 99%.

For instance, if 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.

Referring to the above picture, the red line would the confidence interval and the area below the bell between the upper and lower limits of the interval would be the confidence level.