Chapter 7: Q 1RP. (page 310)
Define sampling error?
When an analyst fails to select a sample that accurately represents the entire population of data, a sampling mistake occurs.
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Explain why increasing the sample size tends to result in a smaller sampling error when a sample means is used to estimate a population mean.
According to the U.S. Census Bureau publication Manufactured Housing Statistics, the mean price of new mobile homes is . Assume a standard deviation of . Let x denoted the mean price of a sample of new mobile homes.
Part (a): For samples of size , find the mean and standard deviation of . Interpret your results in words.
Part (b): Repeat part (a) with .
According to the central limit theorem, for a relatively large sample size, the variable is approximately normally distributed.
a. What rule of thumb is used for deciding whether the sample size is relatively large?
b. Roughly speaking, what property of the distribution of the variable under consideration determines how large the sample size must be for a normal distribution to provide an adequate approximation to the distribution of ?
A statistic is said to be an unbiased estimator of a parameter if the mean of all its possible values equals the parameter; otherwise, it is said to be a biased estimator. An unbiased estimator yields, on average, the correct value of the parameter, whereas a biased estimator does not.
Part (a): Is the sample mean an unbiased estimator of the population mean? Explain your answer.
Part (b): Is the sample median an unbiased estimator of the population mean? Explain your answer.
Suppose that a random sample of size is to be taken from a finite population of size .
a. How many possible samples are there?
b. Identify the relationship between the possible sample means and the possible observations of the variable under consideration.
c. What is the difference between taking a random sample of size from a population and selecting a member at random from the population?
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