### CFA Practice Question

A statistician has framed his hypothesis-testing problem as:

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 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?