Confidence Intervals With z

1. Confidence Intervals With z Statistics 2126

2. 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

3. 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

5. 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

6. 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

8. 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

9. 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

10. 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

13. 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