Applet Exercise Suppose that the population of interest

Chapter 7, Problem 40E

(choose chapter or problem)

Applet Exercise Suppose that the population of interest does not have a normal distribution. What does the sampling distribution of \(\bar{Y}\) look like, and what is the effect of the sample size on

the sampling distribution of  \(\bar{Y}\)? Use the applet SampleSize to complete the following. Use the up/down arrow to the left of the histogram of the population distribution to select the “Skewed” distribution. What is the mean and standard deviation of the population from which samples will be selected? [These values are labeled M and S, respectively, and are given above the population histogram.]

Use the up/down arrows in the left and right “Sample Size” boxes to select samples of size 1 and 3. Click the button “1 Sample” a few times. What is similar about the two histograms that you generated? What is different about them?Click the button “1000 Samples” a few times and answer the questions in part (b). Do the generated histograms have the shapes that you expected? Why?Are the means and standard deviations of the two sampling distributions close to the values that you expected? [Hint: \(\mathrm{V}(\bar{Y})=\sigma^{2} / \mathrm{n}\).]Click the button “Toggle Normal.” What do you observe about the adequacy of the approximating normal distributions?Click on the two generated sampling distributions to pop up windows for each. Use the up/down arrows in the left and right “Sample Size” boxes to select samples of size 10 and 25. Click the button “Toggle Normal.” You now have graphs of the sampling distributions of the sample means based on samples of size 1, 3, 10, and 25. What do you observe about the adequacy of the normal approximation as the sample size increases?

Equation Transcription:

Text Transcription:

\bar Y

\bar Y

V(\bar Y)=\sigma^2 / n