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Confidence Intervals With z. Statistics 2126. Introduction. Last time we talked about hypothesis testing with the z statistic Just substitute into the formula, look up the p, if it is < .05 we reject H 0. Estimation. We could also estimate the value of the population mean
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Confidence Intervals With z Statistics 2126
Introduction • Last time we talked about hypothesis testing with the z statistic • Just substitute into the formula, look up the p, if it is < .05 we reject H0
Estimation • We could also estimate the value of the population mean • Well all we will do in essence is use the data we had, and the critical value of z • The critical value is the value of z where p = .05 • So for a two tailed hypothesis it is 1.96
Back to the table… • What value gives you .025 in each tail? • You could look it up in the entries in the table, or use the handy dandy web tool I talked about last time
So now with the old data from last time let’s estimate the mean • The population mean that is… • = 108 • n = 9 • =15 • z = +/- 1.96
Now be careful… • That is the 95 percent confidence interval for the estimate of • That does not mean that moves around and has a 95 percent chance of being in that interval • Rather, it means that there is a 95 percent chance that the interval captures the mean
Two sides of the same coin • You could use the confidence interval to do the hypothesis test. • Remember our null was that =100 • Well, the 95 percent confidence interval captures 100 so the of our group, statistically, is no different than 100
Making our estimate more accurate • How could we make our estimate more precise? • Increase n • Decrease z • If we decrease z we get more false positives though right
So in conclusion • Confidence intervals allow you to test hypotheses and make estimates • They are affected by the critical value of z and the sample size • We practically can only change the sample size