# 101004u - AGENDA Point Estimation Interval Estimation Tests...

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Sheet1 Page 1 AGENDA Point Estimation Interval Estimation Tests of Hypotheses Null Hypothesis and Tests of Hypotheses Hypotheses concerning one mean POINT ESTIMATION Have an population of unknown mean Take a sample Point Estimator X bar of sample Estimate of error MAXIMUM ERROR OF ESTIMATEVARIANCE KNOWN For a given sized random sample what will be the maximum size of the estimate error MAXIMUM ERROR OF ESTIMATEVARIANCE UNKNOWN For a given sized random sample what will be the maximum size of the estimate error DETERMINATION OF SAMPLE SIZE For a given level of precision (error) we can also determine how many observations need to be in the sample Rearrage the maximum error of estimate equation Must know alpha, E, and sigma May have to estimate sigma INTERVAL ESTIMATION Point estimates are unlikely to correspond to the actual population parameter Preferable to replace point estimates with interval estimates Need to specify a confidence level that the estimate will cover the true parameter INTERVAL ESTIMATION FOR POP. MEAN WITH SIGMA KNOWN 1-alpha level of certainty that the interval will contain the population mean Alpha is typically 0.01 (99 percent certain) 0.05 (95 percent certain) EXAMPLE Random sample N=100 Sigma=5.1 X bar = 21.6 95% confidence interval? [20.6, 22.6] INTERVAL ESTIMATION FOR POP. MEAN WITH SIGMA UNKNOWN 1-alpha level of certainty that the interval will contain the population mean Alpha is typically

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Sheet1 Page 2 0.01 (99 percent certain) 0.05 (95 percent certain) EXAMPLE Random sample N=80 s =5.55 X bar = 18.85 99% confidence interval? [17.25, 20.45]
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101004u - AGENDA Point Estimation Interval Estimation Tests...

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