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Chapter 8: Q 8.1RP. (page 346)

Explain the difference between a point estimate of a parameter and a confidence-interval estimate of a parameter.

Short Answer

Expert verified

Point estimation involvesthe use of sample data to calculate a single value.

The confidence-interval estimate is measured using the point estimate.

Step by step solution

01

Explanation

We try to guess or estimate the unknown value of a population parameter using the value of a statistic in point estimation. This is a single value or point estimate of the parameter. The name point estimate comes from this.

In interval estimate, however, we measure a range within which the population parameter falls, with a confidence level represented in percentages. The point estimate is used to calculate the confidence interval estimate. The percentage indicates our level of certainty that the population parameter falls inside the estimated range.

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Most popular questions from this chapter

Batting Averages. An issue of Scientific American revealed that batting averages, $x$ of major-league baseball players are normally

distributed and have a mean of $0.270$ and a standard deviation of $0.031$ For samples of $20$ batting averages, identify the distribution of each variable.

a. $\frac{\bar{x} - 0.270}{0.031 / \sqrt{20}}$

b. $\frac{\bar{x} - 0.270}{s / \sqrt{20}}$

The value of a statistic used to estimate a parameter is called a ______ of the parameter.

Poverty and Dietary Calcium. Refer to Exercise $8.70$

a. Determine and interpret a $95 %$ upper confidence bound for the mean calcium intake of all people with incomes below the poverty level.

b. Compare your one-sided confidence interval in part (a) to the (twosided) confidence interval found in Exercise $8.70$

M\&Ms. In the article "Sweetening Statistics-What M\&M's Can Teach Us" (Minitab Inc., August $2008$ ), M. Paret and E. Martz discussed several statistical analyses that they performed on bags of M\&Ms. The authors took a random sample of $30$ small bags of peanut M\&Ms and obtained the following weights, in grams (g).

a. Determine a $95 %$ lower confidence bound for the mean weight of all small bags of peanut M\&Ms. (Note: The sample mean and sample standard deviation of the data are $52.040 g$ and $2.807 g$ respectively.)

b. Interpret your result in pant (a).

c. According to the package, each small bag of peanut M\&Ms should weigh $49.3 g$ Comment on this specification in view of your answer to part (b) It provides equal confidence with a greater lower limit.

Part (c) Because the weight of $49.3 g$ is below the $95 %$ lower confidence bound.

State True or False. Give Reasons for your answers..

The confidence interval can be obtained if you know only the margin of error.

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