Sampling Distributions 5.4 ACTIVITY APPLET You can find the interactive applet for this activity at MyLab Statistics. 274 CHAPTER 5 Normal Probability Distributions The Sampling distributions applet allows you to investigate sampling distributions by repeatedly taking random samples from a population. The top plot displays the distribution of a population. Several options are available for the population distribution (Uniform, Bell-shaped, Skewed, Binary, and Custom). Generate random samples of the given size n from the population by clicking 1 time, 5 times, or 1000 times. The sample statistics specified in the bottom two plots will be updated for each sample. When the sample size and number of samples are small enough, the display will show, in an animated fashion, the points selected from the population dropping into the second plot and the corresponding summary statistic values dropping into the third and fourth plots. Click Reset to stop an animation and clear existing results. Summary statistics for each plot are shown in the panel at the right of the plot. Population Sampling Distributions 1 time 5 times 1000 times Reset Info + Select distribution: First statistic: Second statistic: Population Uniform Variance Mean Mean Median Std. dev. 25 25 14.4309 + Samples Sample size Mean Median Std. dev. 0 10 20 30 40 50 Samples 0 0 1 2 3 4 5 6 10 20 30 40 50 Sample means 0 0 1 2 3 4 5 6 10 20 30 40 50 Sample variances 0 0 1 2 3 4 5 6 200 400 600 800 1000 1200 9 + Sample means # of Samples Mean Median Std. dev. + Sample variances # of Samples Mean Median Std. dev. EXPLORE Step 1 Specify a distribution. Specify what summary statistics to display in the bottom two graphs. Specify the sample size n. Step 2 Click 1 time, 5 times, or 1000 times to generate the sampling distributions. DRAW CONCLUSIONS 1. Run the simulation using n = 30 and N = 10 for a uniform, a bell-shaped, and a skewed distribution. What is the mean of the sampling distribution of the sample means for each distribution? For each distribution, is this what you would expect? 2. Run the simulation using n = 50 and N = 10 for a bell-shaped distribution. What is the standard deviation of the distribution of the sample means? Does this agree with the Central Limit Theorem? Is this what you would expect? APPLET
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