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Chapter 7: Problem 3

Bob Ross hosted a weekly television show, The Joy of Painting, on PBS in which he taught viewers how to paint. During each episode, he produced a complete painting while teaching viewers how they could produce a similar painting. Ross completed 30,000 paintings in his lifetime. Although it was an art instruction show, PBS estimated that only \(10 \%\) of viewers painted along with Ross during his show based on surveys of viewers. For each of the following, also identify the population and explain your choice. a. Is the number 30,000 a parameter or a statistic? b. Is the number \(10 \%\) a parameter or a statistic?

Short Answer

Expert verified
a. The number 30,000 is a parameter because it describes a characteristic of the entire population of paintings Bob Ross made. \n\nb. The number 10% is a statistic because it is derived from a subset of the population (surveyed viewers) and used to estimate a characteristic of the entire population (all viewers of the show).

Step by step solution

01

Identifying the Nature of the Value of 30,000

The value 30,000 represents the total number of paintings that Bob Ross completed in his lifetime. This number is a measure that characterizes the whole set or population (i.e., all paintings Bob Ross made). Therefore, it should be considered a parameter.
02

Identifying the Nature of the Value of 10%

The value 10% is an estimate of the proportion of viewers who painted along with Ross during his show. This number is based on surveys, which are usually conducted on a sample, not the entire population. Therefore, it should be considered a statistic.
03

Identification of the Population

For the number 30,000, the population includes all paintings Bob Ross made in his lifetime. For the number 10%, the population refers to all viewers of The Joy of Painting show.

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