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Unformatted text preview: Chapters 5 & 17: Sampling Distribution of Sample Mean and Quality Control Readings: Section 5.2 and Chapter 17 September 10, 2009 1 Sampling Distribution of Sample Mean Sampling Distribution Parameter: describes population Statistic: describes the sample; sampling variability Sampling distribution A probability distribution that characterize the sampling variability The distribution of values taken by a sample statistic, e.g., sample mean, across all possible samples of the same size from the population The sample mean x is most often used as an estimate of the population mean . For a particular sample, sample mean x is a fixed number Imagine taking repeated samples of size n from the population and calculating sample mean for each of them: x 1 , x 2 ,... How are these sample means distributed? How closely to is x ? Sampling Distribution of X = X 1 + X 2 + ... + X n n If X follows a normal distribution with mean and standard deviation , then X is also normally distributed with mean X = and standard deviation X = n What if X is not normally distributed? When randomly sampling from any population with mean and standard deviation , when n is large enough ( > 30), the sampling distribution of X is approximately normal: X N ( , n ) Formula to use for Z : Z = X- X X = X- / n 1 Central Limit Theorem (CLT) Example 1 : In a certain population of fish, the lengths of individual fish follow a normal distribution with mean 54mm and standard deviation 4.5mm. a. What is the probability that a randomly chosen fish is between 51mm and 60mm long? b. Suppose we sample 4 fish. What is the mean and standard deviation of the mean length of these 4 fish? c. What is the probability that the mean length of the 4 fish is between 51mm and 60mm?...
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This note was uploaded on 04/23/2011 for the course STAT 301 taught by Professor Staff during the Spring '08 term at Purdue University-West Lafayette.
- Spring '08