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 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