This preview shows pages 1–3. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: CHAPTER 9 CONFIDENCE INTERVALS 9.1 Confidence Intervals For The Mean When is known If samples are taken from a normally distributed population Then over the long run 95% of the values should be in the interval 96 . 1 ( = population mean = population standard deviation) _____________________________________ 1.96 +1.96 If we now calculated the means of each of these samples the distribution of the sample means would be N( , n ) thus we would expect that if we took repeated samples then 95% of the sample means would be in the interval 1.96 n i.e. within 1.96 standard errors of the mean. This 95% interval can also be written as: P (  1.96 n < x < + 1.96 n ) = 95% Multiplying this inequality by 1 and then adding and x We obtain: P( x 1.96 n < < x + 1.96 n ) = 95% Thus there is a 95% chance that will be in the interval x 1.96 n Example 1 : A sample of size 16 is taken from a normally distributed population and an x = 23 is calculated. Assuming the population has = 5, find a 95% confidence interval for . x 1.96 n = 23 1.96 16 5 = 23 1.96(1.25) = 23 2.45 or (20.55, 25.45). This means we are 95% confident that will be in the interval (20.55, 25.45) Example 2 : A manufacturer claims that their bags of cement have an average weight of 80 lbs. A sample of size 9 is taken and an x = 79 is calculated. Assuming the standard deviation of bag weights is 1 lb find a 99% confidence interval for the...
View
Full
Document
This note was uploaded on 12/05/2011 for the course MATH 2040 taught by Professor Raysievers during the Fall '10 term at Utah Valley University.
 Fall '10
 RaySievers
 Statistics

Click to edit the document details