- CFA Exams
- CFA Level I Exam
- Study Session 3. Quantitative Methods (2)
- Reading 11. Hypothesis Testing
- Subject 8. Hypothesis Tests Concerning the Mean: T-Test vs. Z-Test

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**CFA Practice Question**

A mechanic is concerned that his very expensive pressure gauge is giving faulty readings. He measured 18 pressures with his gauge and then compared them with the actual pressure given. His gauge showed a mean of 120 psi with a standard deviation of 0.75 psi. The actual pressure was 122 psi. The t test statistic is less than the critical value of t for a 90% confidence level. What should the mechanic infer from this?

A. The calibrated gauge understates the real pressure at a 95% confidence interval.

B. The mechanic's gauge understates the real pressure at a 90% confidence interval.

C. The mechanic's gauge readings do not differ from the actual pressure at a 90% confidence interval.

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**User Contributed Comments**
7

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

Nguyen |
why, t-value<critical value --> cannot reject the Null. |

Pooh |
Given that the t-statistic < critical value, the p-value < the significance level of 10%, the effect is statistically significant. Therefore, the null hypothesis is rejected. This means that the Ha is accepted: U1 < U2. |

hizmo |
If you actually calculate the t-statistic, it is actually higher than than the critical value :) |

george2006 |
Don't be fool by the words "less than". It is actually less than the negative critical value of -1.645 ( use z stat value to approximated t value). Do actual calc anyhow to get better understanding of the problem. the words are sometime too ambiguous. |

Shelton |
TS=(120-122)/(0.75/sqrt(18))=-11.31<-1.740=t(17;p=0.05) |

teje |
two-sided test, therefore use +/- 1.645 as your critical values |

endurance |
T test are more appropriate since we don't know the population variance. We have to be more conservative with small samples Critical value t(0,05, 17)=1,74, not 1,645 |