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Chapter 22 Notes Examples

# Chapter 22 Notes Examples - Chapter 22 Notes Examples...

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Chapter 22 Notes Examples Page 1 of 2 Example We believe that the true proportion of all USC students from South Carolina is greater than 0.71. H 0 : p = 0.71 H a : p > 0.71 In a sample of 100 students, 80 are from South Carolina. 80 . 0 100 80 ˆ = = p 02 . 0 value p So, if we took many samples and p = 0.71, we would get results this far or farther from p = 0.71 roughly 2% of the time. We have good evidence against H 0 (and in favor of H a ). So, we would reject the null hypothesis and conclude that the true proportion of USC students from South Carolina is greater than 0.71. Calculating P-values We conduct hypothesis test under the assumption that H 0 is true. If the claim p = 0.71 were true and we tested many random samples of n = 100 students, the sampling distribution of p ˆ would be approximately normal with mean = p = 0.71 and standard deviation = 0454 . 0 100 ) 29 . 0 )( 71 . 0 ( ) 1 ( = n p p Calculating P-values The alternative hypothesis is one-sided (greater than), so the p-value is the probability of getting an outcome at least as large as 80 . 0 ˆ = p . Calculate the standard score of 80 . 0 ˆ = p . 2 98 . 1 0454 . 0 71 . 0 80 . 0 . tan = = = deviation dard s mean n observatio score z Table B says that the standard score 2 is the 97.73 th percentile of a normal distribution. The proportion of data to the left of 2 is 0.9773.

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Chapter 22 Notes Examples - Chapter 22 Notes Examples...

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