A councilwoman is interested in the proportion of all registered voters in her district who favor an increase in taxes to provide more money for education. One thousand such voters are surveyed and 560 favor the tax increase.

A. What is the population of interest?

B. What is the sample?

C. Are the data observed qualitative or quantitative? Why?

D. What parameter is of interest?

E. Give the value of a statistic that would estimate the desired parameter.

F. Consider the statement: "Fifty-six percent (560 out of 1000) of the voters surveyed favor the tax increase." Is this an example of descriptive statistics or inferential statistics? Explain.

G. Give an example of a statistical inference that might be made.

A. The population is the collection of the opinions about the tax increase of all the registered voters in the councilwoman’s district.

B. The sample is the collection of opinions of the1000 voters surveyed.

C. The data observed are the 1000 opinions of the surveyed voters. Since these opinions would be responses such as "in favor", "opposed", "no opinion", etc., they place each voter in a particular category, and are qualitative. To be quantitative, the data must be a numerical measure of some quantity.

D. The parameter of interest is the proportion of all registered voters in her district who favor an increase in taxes to provide more money for education.

E. The sample proportion of registered voters who favor a tax increase, 560/1000 = .56 is the corresponding statistic that estimates the parameter.

F.  Since this statement is summarizing and describing the sample of 1000 voters, it is an example of descriptive statistics.

G. Approximately 56% of all the registered voters favor the tax increase.

• When identifying statistical terms, complete sentences should be used.

• Both populations and samples are collections of data. Be sure to specify what is being measured when identifying either a population or a sample.

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