8.1 Estimating a Population Mean
Point Estimate
estimate a single number, or point.
因为:the mean of the sample mean equals the population mean (μx¯ = μ).
所以:In other words, on average, the sample mean equals the population mean.(即mean of sample mean 有机会等于 population mean) For this reason, the sample mean is called an unbiased estimator of the population mean.
When the two are equal: sample mean (the name of a variable) is referred unbiased estimator population mean
Otherwise, biased estimator
eg:
Called sample mean is an unbiased estimate of the population mean.
Confidence-Interval Estimate
In the known population standard case of deviation, each sample has a set of sample Mean and confidence intervals for the distribution of the sample Mean, whether for sample distribution, Mean sample are normally distributed.
To obtain a sample mean (Point estimate) + known Population Standard Deviation, can simulate a population distribution (Order population mean = sample mean), according to the 68.26-95.44-99.74 rule, one section can be obtained, if x satisfies the population distribution , then x has a 95.44% probability falls within the interval. Because the population is only one mean different, it can be considered that all sample distribution is sliding population distribution, when the population mean when the confidence interval of the sample, sample population also mean confidence interval. So in the end mean actually, I made the n-th sample, obtain n sample mean, the n mean, there 0.9544n values in the population of the confidence interval.
Therefore, after this Sample n obtained, can take any of a confidence level, the total sample mean and the sample mean of the true population mean located within a confidence range of a