CFA Practice Question

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CFA Practice Question

Suppose we are testing the null hypothesis H0:μ = 50 and the alternative Ha:μ != 50 for a normal population with σ = 6. The standard confidence interval for the mean is (51.3, 54.7). Therefore, ______

A. the p-value for the test is greater than 0.05.
B. the p-value for the test is less than 0.05.
C. the p-value for the test could be greater or less than 0.05. It cannot be determined without knowing the sample size.
Correct Answer: B

Recall that a two-sided significance test rejects a hypothesis H0: μ = μ0 exactly when the value μ0 falls outside 1 - a confidence interval for μ. The confidence interval here suggests we should reject H0 in favor of the two-sided alternative given at a = 0.05 because the interval doesn't include 50. Because we reject H0 at a = 0.05, the p-value must be below 0.05.

User Contributed Comments 9

User Comment
vincenthuang we know we should reject H0, but we don't know alfa. How do we know alfa is 0.05? This question is not clear.
bobert This is how I did it:

50 = mean, (51.3+54.7)/2 = 52, and 52 +- 1.7 (51.3,54.7)

The +/- 1.7 is close to the 90% CI(1.645) which is 5% on each tail. so I figured 1.7 is higher than 1.645 therefore the confidence interval is bigger and the tails are smaller.

By their explanation (I think) you have H0 mu=50 and HA mu != 50 (which I take as does not equal...) The question also gives you the end points for the confidence interval. If you know that the null is rejected, (which you do because the null + alternate = all possible answers, and being that null is equal to 1 possibility, the alternate is all the rest) the p-test would be smallest alpha that the null can be rejected at. Without even knowing the .05, you know that if the range is expanded beyond 51.3 down to 50, the tails have to be shorter. therefore B.
Xocrevilo Nice work bobert. The explanation of the answer above reminds me of my why I switched from books to this site: far too opaque and does not make sense.
LoveIvie Where does the +/- 1.7 figure come from?
bidisha i am wondering the same...i got 2.7 from 54.7-52=2.7 and 52-51.3=.7...i think what he did is then avg the 2.7 and .7. Which is 2.7+.7/2=1.7
johntan1979 This is really a good question, really test your understanding about confidence interval and significance level. If the mean you are testing is not even in the confidence interval, DEFINITELY reject null, and p is DEFINITELY <.05
sshetty2 I think it's important to note also that we only know the confidence interval is in fact 95 % per the given information above
dbedford I think you guys are making this more complicated than it needs to be.

1. Ha is a two tail test which means we can use the confidence interval

2. All the answers are based on a 95% confidence interval with alpha at 5%

3. Since Ho = 50 is not in the confidence interval range then we reject Ho and p< .05

4. Whenever Ho is rejected p < alpha. If Ho is in the range then p> alpha.

Therefore B.
shalie 51.3 + 54.7 / 2 = 53
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