Question

From Research Methods and Statistics 5th ed. would you explain to me how to find critical value of z in chapter 8 question 2d?

I found that z=-1.59

Therefore, Z_obt = -1.59

but how do I use Table A.2 to determine Z_cv?

note: I know the answer is -1.65. What I want to know is how do you get that?

Answer 1

In order to find critical value of z, we have to consider level of significance and whether the test is upper tailed, lower tailed, or two tailed test.

Here, the level of significance is 0.05 and the test is lower tailed. So, the critical value of z will be value of z for which area on the left side of this z (rejection region) will be 0.05.

So, to find critical value, we have to look at z table and find z for which area under the curve is close to 0.05. This will be at -1.6, and at probability somewhere between 0.04 and 0.05 (say 0.045), So, the critical value will be -1.645.