For some reason I thought the critical value in this question would be 1.96, not 1.65? In order to test if the mean IQ of employees in an organization is greater than 100, a sample of 30 employees is taken. The sample value of the computed z-statistic = 3.4. The appropriate decision at a 5% significance level is to: Your answer: A was correct! Ho:µ ≤ 100; Ha: µ > 100. Reject the null since z = 3.4 > 1.65 (critical value).
One tailed test Ho: u <= 100 Ha: u > 100 (what you are testing the sample test against) Note the key words “greater than,” something like “not equal to” would imply a two-tailed test. The critical value that corresponds to 5% in the right tail of the normal distribution (as opposed to 2.5% for two tailed) would be 1.65 Contrast with, Ho u = uo Ha u not equal to ua (two tailed) for 90% confidence interval, alpha is 10%, alpha/2 = 5%. Z at 5% is 1.65
I understand that it is a one tailed test, I still don’t see why we use 1.65 I thought it was: 90% CI = 1.56 95% CI = 1.96 99% CI = 2.58 What is the relationship between significance level and the CI? I guess a 5% significance level is not the same as a 95% CI? I just don’t get Quants…
It is about one tailed test and the values are: 90% CI =1.29 95% CI =1.65 99% CI =2.33 For one tailed test you look in the Z-Table and check for 0.90, in the midle, not on the edges. When you find it you connect it with the right side number. For two tailed test when it says 10% significance level, you actually search for 10% / 2=5% so search for 95% figure in the table so you will find 1.65. Hope that nails this concept. Alex.
Thanks Alex, your explanation is good. I think I’m getting it.