Distribution for Sample Mean抽样分布的均值.ppt

Sampling Distributions for a Mean**a sample mean; parameters such as population means don’t have a distribution. Word Lengths – Gettysburg Address The mean length is ? = 4.295. The standard deviation is ? = 2.123. Not Normal. Right skewed. The standard deviation isn’t helpful for finding probabilities. Sampling Distribution: n = 5 The sample mean has a different distribution. It’s called the sampling distribution of the sample mean (for n = 5). The mean of these sample means is 4.165 (pretty close). The standard deviation of these sample means is 0.927 (less variable). It “fills the number line” more completely. The shape is unknown, but appears closer to Normal. Sampling Distribution: n = 5 The mean of these sample means is 4.302 (very close). Sampling Distribution Given: A quantitative population with mean ? standard deviation ? A random sample from the population, where the population is at least 20 times larger than the sample. (Independent trials.) Statistic: The sample mean . This statistic is an unbiased estimate of the parameter ?. Sampling Distribution: Results The distribution of the sample mean has mean (means “unbiased”) standard deviation  shape closer to Normal (but not necessarily Normal) Sampling Distribution: n = 5 Example Sample means from samples of size n = 5 have mean standard deviation  shape closer to Normal (but not Normal – a bit right skewed) Sampling Distribution: n = 5 The mean of these sample means is 4.302 (very close to 4.295). Sampling Distribution: n = 10 Example Sample means from sample of size n = 10 have mean standard deviation  shape closer to Normal  Sampling Distribution: n = 10 The mean of these sample means is 4.305 (very close). Sampling Distribution Example Sample means from sample of size n = 10 have mean standard deviation  shape closer to Normal very close – enough so that a Normal could be used for probabilities Distribution of the