STAT371 DISCUSSION 6 October 13 2002 1 Statistical estimation The estimate of population mean is sample mean y The estimate of population standard deviation is sample standard deviation s 2 The standard error of the mean is s SEy n which is a measure of the reliability or precision of y as an estimate of the smaller the SE the more precise the estimate Consider What is the distincton between standard error and standard deviation 3 Confidence interval The construction of confidence interval If the sample size is n sample mean is y and the standard error is SEy then the 1 confidence interval for is constructed as follows s y t 2 n where the criticl value t 2 is determined from Student s t distribution with df n 1 For instance if 10 then the 90 confidence interval is y t0 5 SEy The interpretation of a confidence interval Suppose the 95 confidence interval of is a b which of the following statement is true Pr a b 95 We are 95 confidence that the population mean is between a and b Pr a y b 95 1 We are 95 confidence that the sample mean y is between a and b If we take 100 samples from the population and construct 100 95 confidence intervals Then there will be 95 confidence intervals containing Pr the next sample will give us a confidence interval that contains 0 95 4 Planning a study to estimate To get a desired standard error the sample size should be n Guessed SD 2 Desired SE Exercise Y follows a normal distribution with mean 20 and standand deviation 2 Take a sample from the population and get these data 19 10672 20 49547 19 20281 16 81740 19 18170 19 44320 18 34311 19 51481 19 22503 25 53221 20 24905 18 80119 21 46908 sx get sample mean Y and sample standard deviation s the sample error Pr 19 Y 22 the 90 confidence interval for if we want the standard error to be less than 0 1 how large should the sample be 2
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