With a two-tailed test at the 5% significance level the critical z-value is (+/-)1.96 With a one-tailed test at the 5% significance level the critical z-value is (+/-)1.645 Is this correct?
Yes it is correct. In the Z-table, look for 0.9505 which is closest to 0.95 and you will see that the corresponding Z = 1.65 for a one-tailed test (BTW you can use either 1.65 or 1.64). Now if you were to see the two tailed test, it means you have 0.025 on one side and another 0.025 on the other side. Therefore in the Z-table look for the number 0.9750 and see the corresponding Z-value which is 1.96. However, instead of doing this during test, it is better to just memorize it. hope if helps. good luck
Thanks for the explanation; How does this relate with the proceeding section on Sampling and Estimation with use of confidence intervals and t values and z values? I’m getting these confused here…
gazhoo, 1. Hypothesis Testing is only an application of Sampling and Estimation. So, the 2 topics are related and not different. 2. Regarding, t and z values, take it this way: they are approximately the same. If I say, t distribution is fatter than z distribution, this may confuse you. But for understanding purpose, t values will give you a bigger range of values for the same confidence level than those coming from z values. Z values are more precise, because they operate on larger sample, better known population variables (populaiton deviation) etc. Whereas, when you dont have enough information about population, t values give you a bigger interval (bigger, more conservative/safe interval). 3. Regarding one/two tail: 90% 2 tail will become 95% one tail. Just draw a distribution and interval on paper, and it should become clearer. Hope it helps. Good Luck.