91Ó°ÊÓ

Briefly explain the meaning of a population probability distribution and a sampling distribution. Give an example of each.

Explain briefly the meaning of nonsampling errors. Give an example. Do such errors occur only in a sample survey, or can they occur in both a sample survey and a census?

The following data give the ages (in years) of all six members of a family. \(\begin{array}{llllll}55 & 53 & 28 & 25 & 21 & 15\end{array}\) a. Let \(x\) denote the age of a member of this family. Write the population probability distribution of \(x\). b. List all the possible samples of size four (without replacement) that can be selected from this population. Calculate the mean for each of these samples. Write the sampling distribution of \(\bar{x}\). c. Calculate the mean for the population data. Select one random sample of size four and calculate the sample mean \(\bar{x}\). Compute the sampling error.

Let \(\bar{x}\) be the mean of a sample selected from a population. a. What is the mean of the sampling distribution of \(\bar{x}\) equal to? b. What is the standard deviation of the sampling distribution of \(\bar{x}\) equal to? Assume \(n / N \leq .05\).

When is an estimator said to be consistent? Is the sample mean, \(\bar{x}\), a consistent estimator of \(\mu ?\) Explain.

How does the value of \(\sigma_{\bar{x}}\) change as the sample size increases? Explain.

Consider a large population with \(\mu=60\) and \(\sigma=10\). Assuming \(n / N \leq .05\), find the mean and standard deviation of the sample mean, \(\bar{x}\), for a sample size of a. 18 b. 90

Explain the central limit theorem.

A population has a distribution that is skewed to the left. Indicate in which of the following cases the central limit theorem will apply to describe the sampling distribution of the sample mean. a. \(n=400\) b. \(n=25\) c. \(n=36\)

A population has a distribution that is skewed to the right. A sample of size \(n\) is selected from this population. Describe the shape of the sampling distribution of the sample mean for each of the following cases. a. \(n=25\) b. \(n=80\) c. \(n=29\)