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Chapter 7: Q.20 (page 431)

A sample of teens A study of the health of teenagers plans to measure the blood cholesterol levels of an SRS of 13- to 16-year-olds. The researchers will report the mean x from their sample as an estimate of the mean cholesterol level M in this population.

(a) Explain to someone who knows no statistics what it means to say that xis an unbiased estimator of 渭.

(b) The sample result x is an unbiased estimator of the population mean 渭 no matter what size SRS the study chooses. Explain to someone who knows no statistics why a large random sample gives more trustworthy results than a small random sample.

Short Answer

Expert verified

a). The average of all possible x炉-values is equal to 渭.

b). A larger sample gives more information and less variability.

Step by step solution

01

Part (a) Step 1: Given Information

A study of the health of teenagers plans to measure the blood cholesterol levels of an SRS of 13- to 16-year-olds.

02

Part (a) Step 2: Explanation

x炉is an unbiased estimator of 渭if the average of all possible values of x炉is equal to 渭.

03

Part (b) Step 1: Given Information

A study of the health of teenagers plans to measure the blood cholesterol levels of an SRS of 13- to 16-year-olds.

04

Part (b) Step 2: Explanation 

A larger sample gives more information about the distribution of values and thus it can be used to make more precise estimates.

More precise results also have less variability in the results.

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