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### 21 Cards in this Set

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 Standard error of the sample means: V(xbar) = v/radical(n)S(xbar) = s/radical(n) (when v is unknown) Maximum or margin error of estimate: 1. E = Z.V (xbar)2. E = t.S (xbar) (when v is unknown)3. E = Z.radical (P(1 - P)/n) for proportion To calculate Z: 1. Divide the comfidence level (CL) by 2:2. Find the nearest value in the body of the Z-table3. Go and find the Z-value Confidence Interval of population mean: Xbar - E =< M =< xbar + EP - E =< Pi =< P + E The best estimate of the population mean is: The sample mean; also called point estimate To construct a CI: 1. Calculate Z by using CL2. Calculate Vxbar3. Calculate E4. Find the CI using M Interpret the CI: 1. The limit of the CI of the population mean are (xbar - E) & (xbar + E)2. We expect that certain% of similarly comstructed CI to contain population mean (or population proportion when P is used) When population SD is unknown: We use sample SD instead:V ===> S Difference between normal distribution and t-distribution: - Normal distribution is bell-shaped- t-distribution is mound shaped Degree of freedom: df = n - 1 As n increases more than 30: t approaches Z To find t: 1. Calculate df2. Use CL by using the t-table Population distribution is normal, sampling distribution of the sample mean is: Normal Population distribution is unknown, the sampling distribution of the sample mean is: 1. n >= 30: guaranteed as normal by CLT2. n < 30: assume population distribution is normal ===> sampling distribution will be normal 1. P:2. Pi: 1. Sample proportion2. Population proportion3. Binomial distribution Sample size (n) to estimate a population mean for Z only: n = (Z. V/E)^2 3 factors to determine sample size for population mean: 1. Margin of error (E)2. Confidence level (to find Z)3. Standard deviation (V) Sample size (n) to estimate a population proportion (P =~ Pi): n = P(1 - P)(Z/E)^2n = Pi(1 - Pi)(Z/E)^2 3 factors to determine the sample size for population proportion: 1. Margin error (E)2. Confidence level (to find Z)3. Proportion or SD for proportion: Vp = P (1 - P) The calculated sample size (n) should always be rounded . . . To the next whole number (up) No estimate of n: P = 0.5