an We emphasize the importance of using a normal probability plot to determine if there is any evidence of nonnormality. If the population is not normally distributed, the sample mean may not be the most efficient estimator of the population mean. In particular, if outliers heavily affect the population distribution, the sample mean is less efficient than other estimators (such as the median). Table 7.1 is a summary of some properties for selected point estimators. It is neither an exhaustive list of estimators nor an exhaustive list of properties that an estimator possesses. Entitatiune Single Population Table 7.1 Properties of Selected Point Estimators u59 POPULATION PALAMETER Mean Mean. POINT ESTIMATOK X Median PROPERTIES Unbiased, most efficient (assuming normality) Unbiased (assuming normality), but not most efficient Unbiased, most efficient Unbiased, most efficient (assuming normality) Proportion, P Variance, o Example 7.2 Price-Earnings Ratios (Estimators) Suppose that we randomly sampled stocks traded on the New York Stock Exchange on a particular day and found the price-earnings ratios of these stocks to be as follows: 10 16 13 11 12 14 12 15 14 14 13 13 Does the normal probability plot suggest non-normality? Find point estimates of the mean and variance. Discuss the properties of these estimators. 13