### CFA Practice Question

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### CFA Practice Question

A hypothesis test at the 5% level of significance, where the population standard deviation is 5.5, is constructed. A random sample of size n = 18 yields a sample mean of 67 and a sample standard deviation of 6. The critical value for H0: μ > 70 is ______.

A. -1.740
B. -1.645
C. 1.740

Because the population standard deviation, σ, is known to be 5.5, we use a normal distribution, z(0.05). Looking in the normal table for 0.05 and reading back to the row and column, we get -1.645. The rejection region is to the bottom 5%, so the critical value is -1.645.

User Comment
oluji why use the z table here when the sample size is less than 30 and the population is not stated as normal. I assumed the t-table is the appropriate tool. Can someone enlighten me?
jade z-test should be used as the population variance (standard deviation) is known!
sapphire Does anybody know how to get -1.645 from the table? What I get is 0.5199. Thanks a lot!
StanleyMo hello sapphire, in fact this consider as two tails test with 5% critical percen at right and left, so for total 10% critial percen it was 1.645. ( 90% confidence interval)
afficionado Oluji, when the distribution is normal and the population variance is known, regardless of the sample, the appropriate statistic is z
johntan1979 The question never stated that the distribution is normal. t test is more appropriate for n<30
gill15 agree -- t test --- this is not right..
Shaan23 Agree with John and Gill. Both have are always spot on when it comes to this stuff.
Shaan23 Actually John and Gill are incorrect here but this question is written poorly.

It doesnt state that it is normally distributed but cause three answers do appear -- we have to assume its normal. If we assume its non-normal also, because the n<30 we would not be able to do T-test or Z-test because they require N>30 for both if NON-NORMAL.

From this logic, since it is normal and we know standard deviation --- use Z test.
lawlee how do we know the rejection region is the top of bottom 5%? Anyone please.