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Chapter 8: Problem 2

Explain the meaning of a point estimate and an interval estimate.

Short Answer

Expert verified
A point estimate is a single value used as a best estimate of the population parameter of interest, while an interval estimate is a range of values that might contain the population parameter. Interval estimates often convey more information about the parameter and its uncertainty than point estimates do.

Step by step solution

01

Understand the Point Estimate

A point estimate is a single data point used as a best guess or best estimate of a parameter of interest in population. For example, the mean, median, or mode of a sample can serve as a point estimate of the mean, median, or mode of the population.
02

Understand the Interval Estimate

An interval estimate is defined as a range, or an interval, used for estimating a parameter of interest. Interval estimates provide more information about the parameter than point estimates. An example of interval estimate is constructing a confidence interval for a population's mean value. A 95% confidence interval might range from 10 to 20, for example. This means that we are 95% certain that the true population value lies somewhere between 10 and 20.
03

Comparing Point and Interval Estimates

While both point and interval estimates are used to estimate a population parameter, they offer different amount of information. A point estimate provides a single most likely value, while an interval estimate provides a range of possible values. Interval estimates are typically preferable to point estimates because they provide a measure of the estimate's precision and its potential error.

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Most popular questions from this chapter

A sample selected from a population gave a sample proportion equal to .31. a. Make a \(95 \%\) confidence interval for \(p\) assuming \(n=1200\). b. Construct a \(95 \%\) confidence interval for \(p\) assuming \(n=500\). c. Make a \(95 \%\) confidence interval for \(p\) assuming \(n=80\). d. Does the width of the confidence intervals constructed in parts a through \(c\) increase as the sample size decreases? If yes, explain why.

A company that produces 8 -ounce low-fat yogurt cups wanted to estimate the mean number of calories for such cups. A random sample of 10 such cups produced the following numbers of calories. \(\begin{array}{lllllllll}147 & 159 & 153 & 146 & 144 & 148 & 163 & 153 & 143 & 158\end{array}\) Construct a \(99 \%\) confidence interval for the population mean. Assume that the numbers of calories for such cups of yogurt produced by this company have an approximately normal distribution.

A mail-order company promises its customers that the products ordered will be mailed within 72 hours after an order is placed. The quality control department at the company checks from time to time to see if this promise is fulfilled. Recently the quality control department took a sample of 50 orders and found that 35 of them were mailed within 72 hours of the placement of the orders. a. Construct a \(98 \%\) confidence interval for the percentage of all orders that are mailed within 72 hours of their placement. b. Suppose the confidence interval obtained in part a is too wide. How can the width of this interval be reduced? Discuss all possible alternatives. Which alternative is the best?

In a random sample of 50 homeowners selected from a large suburban area, 19 said that they had serious problems with excessive noise from their neighbors. a. Make a \(99 \%\) confidence interval for the percentage of all homeowners in this suburban area who have such problems. b. Suppose the confidence interval obtained in part a is too wide. How can the width of this interval be reduced? Discuss all possible alternatives. Which option is best?

A random sample of 20 acres gave a mean yield of wheat equal to \(41.2\) bushels per acre with a standard deviation of 3 bushels. Assuming that the yield of wheat per acre is normally distributed, construct a \(90 \%\) confidence interval for the population mean \(\mu .\)
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