# Reading 12-Hypothesis Testing

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## HYPOTHESIS TESTING

Question | Answer |
---|---|

Hypothesis testing | With reference to statistical inference, the subdivision dealing with the testing of hypotheses about one or more populations. |

Steps in Hypothesis Testing | Stating the hypotheses. Identifying the appropriate test statistic and its probability distribution.Specifying the significance level.Stating the decision rule.Collecting the data and calculating the test statistic.Making the statistical decision.Making the economic or investment decision. |

Definition of Null Hypothesis | The null hypothesis is the hypothesis to be tested. For example, we could hypothesize that the population mean risk premium for Canadian equities is less than or equal to zero. |

Definition of Alternative Hypothesis | hypothesis accepted when the null hypothesis is rejected. Our alternative hypothesis is that the population mean risk premium for Canadian equities is greater than zero. |

two-sided hypothesis test (or two-tailed hypothesis test) | We reject the null in favor of the alternative if the evidence indicates that the population parameter is either smaller or larger than θ0 |

one-sided hypothesis test (or one-tailed hypothesis test) | we reject the null only if the evidence indicates that the population parameter is respectively greater than or less than θ0. The alternative hypothesis has one side. |

Definition of Test Statistic | A test statistic is a quantity, calculated based on a sample, whose value is the basis for deciding whether or not to reject the null hypothesis. |

power of a test | probability of correctly rejecting the null—that is, the probability of rejecting the null when it is false |

Definition of a Rejection Point (Critical Value) for the Test Statistic | A rejection point (critical value) for a test statistic is a value with which the computed test statistic is compared to decide whether to reject or not reject the null hypothesis. |

Definition of p-Value | The p-value is the smallest level of significance at which the null hypothesis can be rejected. |

## HYPOTHESIS TESTS CONCERNING THE MEAN

Question | Answer | Column 3 |
---|---|---|

Test Statistic for Hypothesis Tests of the Population Mean | If the population sampled has unknown variance and either of the conditions below holds | the sample is large, or the sample is small but the population sampled is normally distributed, or approximately normally distributed, |

The z-Test Alternative | If the population sampled is normally distributed with known variance σ2, then the test statistic for a hypothesis test concerning a single population mean, μ | z = (x-uo)/(σ/root(n)) |

Test Statistic for a Test of the Difference between Two Population Means | When we can assume that the two populations are normally distributed and that the unknown population variances are equal, a t-test based on independent random samples is given by | look at formula |

Test Statistic for Tests Concerning the Value of a Population Variance | If we have n independent observations from a normally distributed population, the appropriate test statistic is | look for formula |

Test Statistic for Tests Concerning Differences between the Variances of Two Populations (Normally Distributed Populations) | Suppose we have two samples, the first with n1 observations and sample variance The samples are random, independent of each other, and generated by normally distributed populations. | |

A “not equal to” alternative hypothesis | Reject the null hypothesis at the α significance level if the test statistic is greater than the upper α/2 point of the F-distribution with the specified numerator and denominator degrees of freedom. | |

A “greater than” or “less than” alternative hypothesis | Reject the null hypothesis at the α significance level if the test statistic is greater than the upper α point of the F-distribution with the specified number of numerator and denominator degrees of freedom. | |

Spearman rank correlation coefficient, rS | The Spearman rank correlation coefficient is essentially equivalent to the usual correlation coefficient calculated on the ranks of the two variables (say X and Y) within their respective samples. Thus it is a number between −1 and +1, where −1 (+1) denotes a perfect inverse (positive) straight-line relationship between the variables and 0 represents the absence of any straight-line relationship (no correlation) | |

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