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7.2 Why should you generally expect some error when estimating a parameter (e.g., a population mean) by a statistic (e.g., a sample mean)? What is this kind of error called?

Short Answer

Expert verified

There are some mistakes when estimating the population parameter using the statistic value. This kind of error is called Sampling Error.

Step by step solution

01

Concept introduction

When a critic fails to choose a model that accurately depicts the entire population of data, this is known as a sampling error.

02

Explanation

Calculate the population parameter (a function of population observation, example population means) by a statistic (a function of sample observations example sample means).
Expect some inaccuracies because just a portion of the population is used (i.e. sample).
If the sample contains an outlier (an observation that is very dissimilar to the overall nature of the population observations), the statistic's value will not reflect the true nature of the population, i.e. there will be mistakes, then estimate the population parameter using the statistic's value.
Sampling error is the name for this type of error.
As a result, there are some mistakes when estimating the population parameter using the statistic value. This is known as the Sampling Error.

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Most popular questions from this chapter

Ethanol Railroad Tariffs. An ethanol railroad tariff is a fee charged for shipments of ethanol on public railroads. The Agricultural Marketing Service publishes tariff rates for railroad-car shipments of ethanol in the Biofuel Transportation Database. Assuming that the standard deviation of such tariff rates is \(1,150, determine the probability that the mean tariff rate of 500randomly selected railroad car shipments of ethanol will be within \)100of the mean tariff rate of all railroad-car shipments of ethanol. Interpret your answer in terms of sampling error.

America's Riches. Each year, Forbes magazine publishes a list of the richest people in the United States. As of September l6, 2013, the six richest Americans and their wealth (to the neatest billion dollars) are as shown in the following table. Consider these six people a population of interest.

(a) For sample size of 5construct a table similar to table 7.2 on page293.(There are 6 possible sample) of size 5

(b) For a random sample of size 5determine the probability that themean wealth of the two people obtained will be within 3(i.e,3billion) of the population mean. interpret your result in terms of percentages.

7.1 Why is sampling often preferable to conducting a census for the purpose of obtaining information about a population?

A statistic is said to be an unbiased estimator of a parameter if the mean of all its possible values equals the parameter; otherwise, it is said to be a biased estimator. An unbiased estimator yields, on average, the correct value of the parameter, whereas a biased estimator does not.

Part (a): Is the sample mean an unbiased estimator of the population mean? Explain your answer.

Part (b): Is the sample median an unbiased estimator of the population mean? Explain your answer.

Refer to Exercise 7.3 on page 295 .

a. Use your answers from Exercise 7.3(b) to determine the mean, μs. of the variable x¯ for each of the possible sample sizes.

b. For each of the possible sample sizes, determine the mean, μi, of the variable x~, using only your answer from Exercise 7.3(a).

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