ch. 12_110910 - Discussion section 227 11/09/10 Effect...

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Discussion section 227 11/09/10 Confidence Intervals Point estimates vs. interval estimates Estimates of population parameters can be either point estimates or interval estimates. A point estimate (e.g. sample mean) is precise but likely inaccurate An interval estimate is less precise but likely more accurate. It is a range of sample statistics we could expect to have if we repeatedly conducted hypothesis tests using samples from our population. Confidence interval : an interval estimate based on our sample mean that includes the population mean a certain percentage of the time (e.g. 95%) if we were to sample from the same population repeatedly. Calculating confidence intervals: Z distribution Remember that we use a z test when we know that SD and M of the population. Example: Let’s say μ = 72, σ = 10, M = 75, n = 40 and we want to calculate a confidence interval around this mean. 1. Draw a sampling distribution and put the sample mean in the middle, not the population mean. Write the percentage area under the curve. 2. In your z table, find the area under the curve corresponding to 47.5% and write the corresponding z scores (±1.96 as you may remember). 3. Now, turn the z scores into raw scores. It is important to remember that we are calculating an interval around our sample mean and so we use it in our calculation – not the population mean. Second, because we have a sample mean rather than an individual score, we use a distribution of means and so we need to calculate the standard error: σ/√n = 10/√40 = 1.58
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Next, use the Z score formula to find the value for the sample means at each end of the distribution. Remember that our original Z score formula was: Now we are solving for M (lower) and M (upper) and using M (sample) instead of the population mean: Our confidence interval is then reported in parenthesis (71.9, 78.1). To summarize:
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ch. 12_110910 - Discussion section 227 11/09/10 Effect...

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