Reconciling confidence intervals and hypothesis testing

Guys I have a question about reconciling the results of CIs and hypothesis testing. Consider this problem:,702869 As one person notes: z(0.05) = (10.05%-10%)/(0.01%/sqrt(30)) = 27.39 > 1.645 therefor reject the null Therefore at the 5% level of significance we can reject the null in favor of the alternative hypothesis. But let’s build a 95% confidence interval for the mean. This will be 10.05% +/- (1.96)*(.01%/sqrt(30) = a confidence interval that ranges from 10.0464215 to 10.0535785. Meaning that we are 95% confident that the value of the population mean falls between these values. How does one reconcile this conceptually with the results from hypothesis testing?

you seem to be getting confused between a 1-tailed and a 2-tailed hypothesis test and the CI for the mean/ the first 1.645 with 0.05 level of significance is a 1-tailed test statistic. the 1.96 is a 5% 2-tailed CI --> so on the right and left of your CI - you only have 0.025 in the tail. (2.5% in the tail). Hope that helps you. CP