6-3 Sampling Distributions and Estimators 273 Proportions Sample 1 Sample 2 Sample 3 (Population Proportion is p) Distribution of Sample Proportions Sample Proportions Sample Sample proportions tend to have a normal distribution pˆ pˆ pˆ pˆ pˆ pˆ pˆ pˆ pˆ pˆ pˆ pˆ pˆ pˆ pˆ pˆ pˆ pˆ pˆ pˆ • • • 1 pˆ 2 pˆ 3 pˆ Sampling Procedure: Randomly select n values and find the proportion p for each sample. ˆ Means Sample 1 Sample 2 Sample 3 (Population Mean is m) Distribution of Sample Means Sample Means Sample Sample means tend to have a normal distribution • • • Sampling Procedure: Randomly select n values and find the mean x for each sample. x x x x x x x x x x x x x x x x x X1 X2 X3 x x x x x Variances Sample 1 Sample 2 Sample 3 (Population Variance is s2) Distribution of Sample Variances Sample Variances Sample Sample variances tend to have a skewed distribution • • • Sampling Procedure: Randomly select n values and find the variance s2 for each sample. s2 1 s2 2 s2 3 s2 s2 s2 s2 s2 s2 s2s2s2s2s2s2 s2s2s2s2s2s2 s2 s2 s2 s2 s2s2s2s2s2 FIGURE 6-16 General Behavior of Sampling Distributions FIGURE 6-17 Histogram of 50,000 Sample Proportions
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