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Chapter 7: Problem 11

Chapman University conducts an annual Survey of American Fears. One of the objectives of this survey is to collect annual data on the fears, worries, and concerns of Americans. In 2017 the survey sampled 1207 participants. One of the survey findings was that \(16 \%\) believe that Bigfoot is a real creature. Identify the sample and population. Is the value \(16 \%\) a parameter or a statistic? What symbol would be use for this value?

Short Answer

Expert verified
The sample for this study includes 1207 participants surveyed by Chapman University. The population encompasses all Americans. The value \(16 \%\) is a statistic because it is derived from the sample, not the entire population. The symbol used for this value would be '\(\hat{p}\)' signifying the sample proportion.

Step by step solution

01

Identify the Sample

The sample refers to the subset of the population which is selected for study. In this case, 1207 participants who were surveyed by Chapman University are the sample.
02

Identify the Population

The population refers to the whole set of items or individuals of interest. In this context, the population would be all Americans, as the survey aims to collect information about the fears, worries, and concerns of Americans.
03

Distinguish Between Parameter and Statistic

A parameter is a value that describes a characteristic of a population, while a statistic describes a characteristic of a sample. In this problem, the \(16 \%\) who believe Bigfoot is real is derived from the sample (not the entire American population), so this is a statistic.
04

Identify the Symbol for the Value

The symbol commonly used to represent a percentage or proportion in statistics is 'p'. Since it is a statistic derived from a sample, in this case, we can use '\(\hat{p}\)' to denote the \(16\%\) of people who believe in Bigfoot. Here, '\(\hat{p}\)' is the sample proportion.

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Most popular questions from this chapter

According to a Gallup poll, \(45 \%\) of Americans actively seek out organic foods when shopping. Suppose a random sample of 500 Americans is selected and the proportion who actively seek out organic foods is recorded. a. What value should we expect for the sample proportion? b. What is the standard error? c. Use your answers to parts a and b to complete this sentence: We expect \(_____ \%\) of Americans to actively seek out organic foods when shopping, give or take _____ \(\%\) d. Would it be surprising to find a sample proportion of \(55 \%\) ? Why or why not? e. What effect would decreasing the sample size from 500 to 100 have on the standard error?

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You need to select a simple random sample of four from eight friends who will participate in a survey. Assume the friends are numbered \(1,2,3,4,5\), 6,7, and 8 . Select four friends, using the two lines of numbers in the next column from a random number table. Read off each digit, skipping any digit not assigned to one of the friends. The sampling is without replacement, meaning that you cannot select the same person twice. Write down the numbers chosen. The first person is number 7 .$$\begin{array}{lll}07033 & 75250 & 34546 \\\75298 & 33893 & 64487\end{array}$$ Which four friends are chosen?
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