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confidence intervals

# confidence intervals - ` 42 Confidence Intervals Confidence...

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` 42 Confidence Intervals Confidence Intervals are estimates of population parameters, a range (or interval) of values that is likely to contain the true value with X% confidence. They are created to answer the question, How good is our point estimate (mean or proportion or variance) at estimating the population value? (µ - E to µ + E) is the form for a confidence interval for a mean; (p - E to p + E) is the form for a confidence interval for a proportion. The margin of error or the maximum error of estimate is E : For Means: 1. For n > 30 and ∂ known or ∂ unknown (use s, the sample standard deviation): OR If = .05, then p = .05 that µ is outside the bounds set. The term () is the z score that leaves .025 area in the right tail so that z = 1.96 is the critical value used in the formula for = . 05. There is 95% confidence that the true mean lies inside the interval of µ - E to µ + E, where z = 1.96 is used in the formula for the z-score. Example : Find a 99% confidence interval for the mean of 84.2 on a mathematics placement test from a sample of size 40 with a standard deviation of 7.3. is .01 and z for .005 in the right tail is 2.575, so , approximately. The 99% confidence interval is: 84.2 3.0 (rounded of from 2.97) gives, 81.2 < µ < 87.2 . There is a probability of .99 that the true or theoretical mean is inside the interval given.

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