9.1%2c9.2%2c9.3 confidence intervals

9.1%2c9.2%2c9.3 confidence intervals - CHAPTER 9 CONFIDENCE...

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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...
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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.

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9.1%2c9.2%2c9.3 confidence intervals - CHAPTER 9 CONFIDENCE...

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