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**CFA Practice Question**

A realty firm has a large number of condos to rent. The 240 months prior to this year, the average vacancy rate measured every month has been 9.48% and the standard deviation has been 3.5%. Assume that the past 240 months are 'stable', so that the mean and standard deviation measured are true population parameters.

During the current year (12 months) the average vacancy rate measured every month has been 11.06%. t-distributed with 11 dof test statistic for 5% one-tailed = 1.796 z-distributed test statistic for 5% one-tailed = 1.645. Would you reject the Null Hypothesis that the current 12 months are no different from the past 240 months?

A. Yes.

B. No.

C. Insufficient information.

**Explanation:**As the true population standard deviation under the Null is known, you should use the z-test. The test statistic = (11.06% - 9.48%)/(3.5%/(12^0.5)) = 1.5638 is too small for rejecting the Null hypothesis.

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**User Contributed Comments**
5

User |
Comment |
---|---|

andrewmorgan |
I disagree, we dont know if the population is a normal distribution so insufficient information |

Coowy |
i tought its a two-tailed test and therefore the z-test t-statistic are insufficient...??? |

catsong |
Yes it is a two-tailed test. The test statistic for a 5% one tail test is the same for a 10% two tail test, so we re-use the value 1.645, which is larger than the calculated test statistic of 1.5638, so we fail to reject the null. The answer is correct. |

birdperson |
it should be a 2-tail test, H0: mu = x-bar H1: mu does not = x-bar |

michaeloa3 |
andrewmorgan: we already know the population standard deviation so you should not care if it's normal or not. |