CFA Practice Question
A statistician has framed his hypothesis-testing problem as:
H1: mean < 100
H0: mean >= 100
H1: mean < 100
Specify the region for the p-statistic which will lead to the rejection of the null at the 80% significance level.
A. z-statistic < -0.84
B. z-statistic < -1.645
C. z-statistic < -1.35 or z-statistic > +1.35
Explanation: Since the alternative is directional and to the left, we use a left-tailed test. For this, the critical value at the 80% level is -0.84 (-0.84 is the value above which 80% of the probability mass of the standard normal distribution lies). The rejection region is then given by z-statistic < -0.84.
User Contributed Comments 10
| User | Comment |
|---|---|
| cgeek | how do you know 80% is 0.84? |
| KD101 | I agree you can only remember 90% 95% 99% and 1, 2 and 3 std dev values |
| gruszewski | u can reason, that that the level of significance is less strict than for -1,645 and must be less than zero and directional, so only answer a fits |
| steved333 | You're going to get sections of tables where needed. Part of the point is for you to be able to use them. |
| dcsmith | any one keen to take a break for a bit? |
| jpducros | Agree with gruszewski. This is a one tailed test, so you know that for a 95% confidence interval, z = -1,65. If you reduce the confidence interval, the z value is higher...so only answer A is valid. |
| DariSH | Another way to calc it: for two-tailed test we know, that 68% of observations lie within 1st.dev. of the mean. And around 32% are in tails. What we have here is 1 tailed test, so, this means that only 16% observations are in the only tail. This makes 84% of observations to fall into 1 st. dev. of the 1-tailed test. |
| DariSH | Continuing... And 80% significance is smaller than 84%, so it should be less than 1 st. dev. The only answer that returns z that is less than 1 is A. |
| Sandar | can we use fx-991 MS? in that case ..press mode for 2 times..chose SD..then Shift+ 3 .. P ( left tailed), Q (right tailed), R ( 2 sided tails) |
| chenyr05 | how to understand "the rejection of the null at the 80% significance level"? Is alpha = 80% or 20%, isn't alpha the denotation of the significance level? |