stat extra

# stat extra - Kyle Daniele Extra Credit Example 1 Look at...

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Kyle Daniele Extra Credit Example 1 Look at the 95% confidence interval of a proportion, p, if p-hat=.3 and a. n = 30 95% CI = (.13602, .46398) b. n = 100 95% CI = (.21018, .38982) Since the width of the interval in this case is 2[z(1-c)/2(square root of p-hat times q-hat divided by n)], the increase from n = 30 to n = 100 results in a narrower confidence interval since all other quantities remain the same. Example 2 If a sample proportion is given as .35 with a margin of error of +-3%, find the 95% confidence interval for the population proportion. Solution: .35 +- .03 95% confidence interval is (.32, .38) Example 3 A simple random sample of 100 eighth graders at a large suburban middle school indicated that 83% of them are involved with some type of after-school activity. Find the margin of error for this sample result if we are to have 90% confidence in the results. Solution: Check Assumptions. Simple random sample? Given Large population? Given n*p-hat>10 and n*q-hat>10 100(.83) = 83; 100(.17) = 17 Therefore, the margin of error for this sample with 90% confidence is Z(1-C)/2(square root of p-hat times q-hat divided by n) 1.645(square root of .83(1-.83) divided by 100) = .062

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stat extra - Kyle Daniele Extra Credit Example 1 Look at...

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