Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
BA 253: Business Statistics Today More Normal Finish ICE 4 Weds Ch 7: Sampling Distributions Start ICE 5 9/26/12 Fri ICE 5 ↑ Descriptive Statistics: Summarize Data ↑ ↓ Inferential Statistics: Estimate Population from Sample ↓ Chapter 7: Sampling and Sampling Distributions Ex: Collect n data, calculate sample mean = x = point estimate. Use simple random sample. Is x ≈ μ??? That is the question! The approximation gets better as the sample size, n, increases. How is x distributed? In other words, what is the probability distribution of the sample mean? Guess = _________________ Central Limit Theorem For large sample sizes (typically, n ≥ 30), the sample mean x is approximately normally distributed. CLT is true regardless of the original distribution of the data. As n↑, the standard deviation decreases. (That is, x gets closer to μ.) This is why the normal distribution is so common and so important. Show “CLT in Action” Sampling Distribution of x The sample mean, x , has mean μ, standard deviation and is n o Normally distributed if the underlying distribution is Normal. o Approximately Normally Distributed whatever the underlying distribution is if n ≥ 30. o As the sample size increases, n ↑, the sample mean gets closer and closer to the population mean, x ≈ μ. Ex: Normal with mean 100 and sd 20. ICE 5 Do on TI-83. Math, PRB, randNorm(100,20) – try it! 132, 104, 98, 137, 81, etc. How close is your result to 100? Is one data point enough? No. Get 5 numbers, then average. Closer. On Excel, get 30, 100, 1000 numbers and then average. As sample size increases, the approximation gets better.