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Unformatted text preview: sample size n increases, the variance decreases, and the distribution becomes more concentrated around the population mean. A standardized normal random variable can be stated: Z= X−μ X−μ
~ N(0 , 1)
se( X ) σ
n Probability statements about the mean can now be considered. 6 Chapter 7 Example: Exercise 7.17, page 253. Times spent studying by students in the week before final exams follow a normal distribution with standard deviation 8 hours. A random sample of 4 students was taken in order to estimate the mean study time for the population of all students. Questions and Answers (a) What is the probability that the sample mean exceeds the population mean by more than 2 hours ? That is, find: P( X > μ + 2) With n = 4 the standard error of the sample mean X is: se( X ) = σ n = 8 2 = 4 Write the problem as a probability statement about the standard normal random variable Z: ⎛ X − μ (μ + 2 ) − μ ⎞
P( X > μ + 2 ) = P⎜
⎜ se( X ) > se( X ) ⎟
= P Z > 24 ( ) = 1 − P(Z < 0.5) by symm...
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This note was uploaded on 02/06/2014 for the course ECON ECON 325 taught by Professor Whistler during the Spring '10 term at The University of British Columbia.
- Spring '10