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8 Cards in this Set
- Front
- Back
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The Central Limit Theory –
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- Is, given the distribution of the population have mean, u and standard deviation, o.
- The sample size n is large enough - The distribution of the sample mean is approximately normal with mean u and the standard deviation = o/√n - So given that the population has the mean and SD, n is large enough, and the distribution is normal with mean and standard deviation - Assumptions – * sample mean is equal to the population mean * standard deviation of the distribution is o√n * sample distribution is approximately normal as n approaches o0 - Z = (xbar - u) / (o/√n) * has a normal distribution with a mean of 0 and a standard deviation of 1 - The information about x-bar is used to make inference for the population mean u |
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Point Estimation –
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• Use a simple sample statistic to estimate a parameter of interest
o x –bar used to infer u • Odds = p/(1-p) • Advantages of Point Estimation o Its simple o Can use the point estimates in other calculations • Disadvantages of Pont Estimation o Point estimation varies from sample population to sample population o Does not account for variability in estimator |
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Interval Estimation –
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• Provides a range of reasonable values that are intended to contain the parameter of interest, with some confidence level
o Confidence Intervals • A 95% C.I. means, if 100 samples are chosen from the population and 100 different C.I.’s are calculated, then approx. 95 of the intervals would contain the parameter of interest and 5 would not |
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Confidence Intervals (C.I) –
• Two-Sided C.I.’s |
- Has upper and lower limits
- General Two-Sided C.I. Formula for Z-score – [(xbar – Z/2(o/√n) , (xbar + Za/2(o/√n)] - General Two-Sided C.I. Formula for t-score – [(xbar – ta/2(s/√n) , (xbar + ta/2(s/√n)] - The 95% C.I for Z-score – (xbar – 1.96(o/√n) , xbar + 1.96(o/√n)) - The Length of the two-sided C.I. is 2*(Za/2(o/√n)) - The greater the alpha (a), the wider the interval |
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Confidence Intervals (C.I) –
• One-Sided C.I.’s |
- We want an upper OR a lower limit, not both
- The general one-sided formula – u = xbar ± Za(o/√n) OR u = xbar ± ta(s/√n) |
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Confidence Intervals (C.I) –
• The Z and t statistics – |
Z = (xbar - u) / (o/√n)
Used when o is known t = (xbar - u) / (s/√n) Used when o is UNknown |
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Part 6 – C.I., t-distribution, z-distribution
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- As n increases, (o/√n) or (s/√n), the standard errors, decrease.
- This causes the confidence interval to become narrower - Formula to calculate n – n = √([CV() σ)/(.5(C.I.Length)] |
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Part 6 – C.I., t-distribution, z-distribution
• The t-distribution – |
o Like the normal distribution, it is unimodal & symmetric around a mean = 0
o However, t-distribution has thicker tails than the normal distribution because of the additional variability added by the use of “s”, the sample standard deviation o df – the degrees of freedom – * a measure of the amount of info available in the data that can be used to estimate the population variance, o2, • df = (n-1) o so, as n increases, the estimate of 2 improves - For each degree of freedom (df), there is a corresponding t-distribution - As the df’s increase, the t-distribution approached a normal distribution |
