Solved: Applet Exercise What is the effect of the sample

Chapter 7, Problem 8E

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Applet Exercise What is the effect of the sample size on the sampling distribution of S2? Use the applet VarianceSize to complete the following. As in some previous exercises, the population to be sampled is approximately normally distributed with \(\mu=16.50 \text { and } \sigma=6.03\)

What is the value of the population variance \(\sigma^{2}\)?Use the up/down arrows in the left “Sample Size” box to select one of the small sample sizes that are available and the arrows in the right “Sample Size” box to select a larger sample size.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 (i).Are the means of the two sampling distributions close to the value of the population variance? Which of the two sampling distributions exhibits smaller variability?Click the button “Toggle Theory.” What do you observe about the adequacy of the approximating theoretical distributions?Select sample sizes of 10 and 50 for a new simulation and click the button “1000 Samples” a few timesWhich of the sampling distributions appear to be more similar to a normal distribution?Refer to Exercise 7.7(f). In Exercise 7.97, you will show that, for a large number of degrees of freedom, the \(\mathrm{X}^{2}\) distribution can be approximated by a normal distribution. Does this seem reasonable based on your current simulation?

Equation Transcription:

   

Text Transcription:

\mu=16.50 \and \sigma=6.03

\sigma^2

X^2