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Interval estimates and differences

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1. What is the difference between a point estimate and an interval estimate of a parameter? Which is better? Why?
2. What information is necessary to calculate a confidence interval? Is the size of the population relevant when one is determining the sample size for a confidence interval? What is necessary to determine the sample size?
3. A researcher is interested in estimating the average salary of fire fighters in a large city. He wants to be 95% confident that his estimate is correct. If the standard deviation is $1050, how large a sample is needed to get the desired information and to be accurate within $200?
4. A sample of the math test scores of 35 fourth-graders has a mean of 82 with a standard deviation of 15.
a. Find the 95% confidence interval of the mean math test scores of all fourth-graders.
b. Find the 99% confidence interval of the mean math test scores of all fourth-graders.
c. Which interval is larger? Explain why.

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Solution Preview

1. What is the difference between a point estimate and an interval estimate of a parameter? Which is better? Why?

Solution:

A point estimate is a specific numerical value estimate of a parameter. The best point estimate of the population mean m is the sample mean. The advantage of point estimate is that it is one specific number so easier to interpret and understand.

An interval estimate of a parameter is an interval or a range of values used to estimate the parameter. This estimate may or may not contain the value of the parameter being estimated.

If simplicity is preferred (i.e., explaining data to a non-statistician) a point estimate might be better, but the ...

Solution Summary

The solution examines interval estimates and differences between a parameter. The relevant population is determined.

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