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Chapter 7: Q. 7.1 (page 295)

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

Short Answer

Expert verified

The cost of sampling is lower than the cost of census. Furthermore, a census takes longer than sampling.

Step by step solution

01

Given information

To determine the sampling often preferable to conducting a census for the purpose of obtaining information about a population.

02

Explanation

Since conducting an enumeration is ideal for every investigation, many populations are too large to consider gathering data from every part.
Gathering information from a small part of the population and analyzing the results is significantly faster and less expensive.
Yet, sampling might lead to erroneous or misleading results.
Bigger sample size is preferable in general since more information about the population may be gathered.

As a result, the cost of sampling is lower than the cost of census.
Furthermore, a census takes longer than sampling.

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Most popular questions from this chapter

Consider simple random samples of size n without replacement from a population of size N.

Part (a): Show that if n≤0.05N,then0.97≤N-nN-1≤1,

Part (b): Use part (a) to explain why there is little difference in the values provided by Equations (7.1)and (7.2)when the sample size is small relative to the population size- that is, when the size of the sample does not exceed 5% of the size of the population.

Part (c): Explain why the finite population correction factor can be ignored and the simpler formula, Equation (7.2), can be used when the sample size is small relative to the population size.

Part (d): The term N-n/N-1is known as the finite population correction factor. Can you explain why?

7.49 Mobile Homes. According to the U.S. Census Bureau publication Manufactured Housing Statistics, the mean price of new mobile homes is \(65,100. Assume a standard deviation of \)7200. Let x~ denote the mean price of a sample of new mobile homes.
a. For samples of size 50, find the mean and standard deviation of x¯. Interpret your results in words.
b. Repeat part (a) with n=100.

Does the sample size have an effect on the standard deviation of all possible sample means? Explain your answer.

NBA ChampsThe winner of the 2012-2013 National Basketball Association (NBA) championship was the Miami Heat. One possible starting lineup for that team is as follows.

a. Determine the population mean height, μ, of the five players:

b. Consider samples of size 2 without replacement. Use your answer to Exercise 7.11(b) on page 295 and Definition 3.11 on page 140 to find the mean, μx¯, of the variable x¯.

c. Find μx¯using only the result of part (a).

Refer to Exercise 7.10 on page 295.

a. Use your answers from Exercise 7.10(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, μs, of the variable x¯, using only your answer from Exercise 7.10a).
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