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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

Ethanol Railroad Tariffs. An ethanol railroad tariff is a fee charged for shipments of ethanol on public railroads. The Agricultural Marketing Service publishes tariff rates for railroad-car shipments of ethanol in the Biofuel Transportation Database. Assuming that the standard deviation of such tariff rates is \(1,150, determine the probability that the mean tariff rate of 500randomly selected railroad car shipments of ethanol will be within \)100of the mean tariff rate of all railroad-car shipments of ethanol. Interpret your answer in terms of sampling error.

Baby Weight. The paper "Are Babies Normal?" by T. Clemons and M. Pagano (The American Statistician, Vol. 53, No, 4. pp. 298-302) focused on birth weights of babies. According to the article, the mean birth weight is 3369 grams (7 pounds, 6.5 ounces) with a standard deviation of 581 grams.
a. Identify the population and variable.
b. For samples of size 200, find the mean and standard deviation of all possible sample mean weights.
c. Repeat part (b) for samples of size 400.

What is the sampling distribution of a statistic? Why is it important?

7.67 Brain Weights. In 1905, R. Pearl published the article "Biometrical Studies on Man. 1. Variation and Correlation in Brain Weight" (Biometrika, Vol. 4, pp. 13-104). According to the study, brain weights of S wedish men are normally distributed with a mean of 1.40kg and a standard deviation of 0.11kg

a. Determine the sampling distribution of the sample mean for samples of size 3 Interpret your answer in terms of the distribution of all possible sample mean brain weights for samples of three Swedish men.

b. Repeat part (a) for samples of size 12

c. Construct graphs similar to those shown in Fig. 7.4on page 304 .

d. Determine the percentage of all samples of three Swedish men that have mean brain weights within 0.1kg of the population mean brain weight of 1.40kg. Interpret your answer in terms of sampling error.

e. Repeat part (d) for samples of size 12

In Exercises 7.3-7.10, we have given population data for a variable. For each exercise, do the following tasks.
a. Find the mean, 渭, of the variable.
b. For each of the possible sample sizes, construct a table similar to Table 7.2 on page 293 and draw a dotplot for the sampling distribution of the sample mean similar to Fig. 7.1 on page 293.
c. Construct a graph similar to Fig. 7.3 and interpret your results.
d. For each of the possible sample sizes, find the probability that the sample mean will equal the population mean.
e. For each of the possible sample sizes, find the probability that the sampling error made in estimating the population mean by the sample mean will be 0.5or less (in magnitude), that is, that the absolute value of the difference between the sample mean and the population mean is at most 0.5.
7.4 Population data: 2,5,8.
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