- CFA Exams
- CFA Level I Exam
- Study Session 3. Quantitative Methods (2)
- Reading 11. Hypothesis Testing
- Subject 6. The Decision Rule

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**CFA Practice Question**

A poll of 100 randomly sampled adult Americans found that 53% supported banning handgun sales. A newspaper wants to use this data to conclude that a majority of Americans support banning handgun sales. At the 10% level of significance, the newspaper's conclusion should be that ______

A. a majority, p > 50%, of adult Americans support a ban on handgun sales.

B. there is evidence that 53% of adult Americans support a ban on handgun sales.

C. there is no evidence that a majority, p > 50%, of adult Americans support a ban on handgun sales.

**Explanation:**The hypothesis test would appear as shown below:

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**User Contributed Comments**
11

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

danlan |
Where comes the value 1.28? |

danlan |
1.28 from z-table |

ahmado |
why is 0.5*(1-0.5) the variance? |

Mariecfa |
The test statistic, 1.28 is the t-test since the standard deviation is unknown. This is a proportion sample test so we use .5 for the proportion parameter. |

Thecatz |
isn't it (0,53-0,5)/(square root of(np(1-p)/n)) so it is 0,4 no ? |

teje |
since the sample size is fairly large, despite the fact that population standard deviation is unknown, we can still use t or z test. although the t test would be more conservative. |

nostalgia |
the explanation given raises more questions than it answers |

Shaan23 |
TheCats its p(1 - p) /n not np(1 - p) / n |

alles |
shouldn't variance be ((0.53*0.47)/100)^0.5 ? |

lawlee |
I don't understand the p(1-p)/n, can someone kindly explain |

DRamirez |
p(1-p) is the variance of a bernoulli random variable. but since the survey is repeated (n = 100), this should be a binomial random variable with variance: np(1-p). the answer is still C though. |