- CFA Exams
- CFA Exam: Level II 2021
- Study Session 2. Quantitative Methods (1)
- Reading 4. Introduction to Linear Regression
- Subject 5. Testing the significance of a regression coefficient

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**CFA Practice Question**

The manufacturers of a chemical used in flea collars claim that under standard test conditions each additional unit of the chemical will bring about a reduction of 5 fleas (i.e., where X(j) = amount of chemical and Y(J) = B(0) + B(1) x X(J) + E(J), H(0): B(1) = -5)

Suppose that a test has been conducted and results from a computer. include: Intercept = 60, Slope = -4, Standard error of the regression coefficient = 1.0, Degrees of Freedom for Error = 2000, 95% Confidence Interval for the slope -2.04, -5.96.

Is this evidence consistent with the claim that the number of fleas is reduced at a rate of 5 fleas per unit chemical?

Correct Answer: Yes

t(calculated) = (-5 - (-4))/1 = -1, t(critical) = -1.96

Since t(calc) < t(crit) we retain the null hypothesis that B(1) = -5.

Most simply, since -5 is included in the confidence interval for the slope, we can conclude that the evidence is consistent with the claim at the 95% confidence level.

Using a t test: H(0): B(1) = -5, H(A): B(1) ≠ -5

t(calculated) = (-5 - (-4))/1 = -1, t(critical) = -1.96

Since t(calc) < t(crit) we retain the null hypothesis that B(1) = -5.

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**User Contributed Comments**
15

User |
Comment |
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kaliokale |
can anyon explain this question and answer in details>? |

lockedin |
Confidence interval: We are 95% certain that each additional unit of chemical will cause a reduction of between -2.04 (which would translate into a gain of 2.04) and 5.96 fleas. The company claims a reduction of 5 fleas. 5 is within the confidence interval, so we can be 95% certain the company's claims are correct. |

DAS11 |
Thanks lockedin! |

ehc0791 |
well, evidence is not enough to reject H(o), but it doesn't mean H(o) should be accepted. ie. it doesn't mean the claim is true. |

steved333 |
It absolutely is true. When you develop your confidence interval, the point is to say that your H(o) will be rejected as long as you are 95% certain that the case is what H(a) states. As long as the calculated value falls within that interval, it fits the outlined definition of the term "true"- in this case "true" is defined as: with a 95% certainty that the stated amount will be within the calculated range. |

bmeisner |
Steve in statistics you never accept something as true. For the purposes of this question the evidence is "consistent" with the hypothesis but this means only that the test fails to reject H(0) with 95% confidence, not that the hypothesis is actually "true". |

rufi |
bmeisner is right |

quantwannabe |
I thought test statistic is t = [-4 -(-5)]/1 = 1 And the critical value t is +/-1.96 for 5% level of significance (95% confidence level) Null Hypotheses is rejected if test statistic is greater than +critical value or less than -critical value. In our case +1 is neither greater than +1.96 nor smaller than -1.96. Therefore, we can't reject null hypothesis and we must retain the null hypotheses H(o): B(1) = -5 |

annwwar |
Where does this equation come from? t(calculated) = (-5 - (-4))/1 = -1 |

mazen1967 |
t=(b-bbar)/sd of b |

bhaynes |
steved333 is wrong, bmeisner is right. We never accept the null hypothesis. We either reject it or we fail to reject it. |

pb09 |
I truly despise statistics... |

pb09 |
...but I love investments, so I guess I gotta memorize this junk |

cfaajay |
quantwannabe has explained it in consistency with what all is written in book ,over here as per the value of test statistic and the corresponding confidence interval ,the null hypothesis can't be rejected,hence company claim of reduction by 5 fleas is correct (as per our research additional unit of chemical should cause reduction by 4 fleas and as null hypothesis should be the one which should be rejected ,our null hypothesis will be that additional unit will cause reduction by 5 fleas (against our test results ) ,but the confidence interval confirms that our test result are not correct and we can not reject company's claim of reduction of 5 fleas by additional unit of chemical )..so answer is Yes...hope this make sense. |

birdperson |
fail to reject the null is not the same as accepting the null as true |