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# stat I - exam III

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

When we conduct a formal statistical study to test a hypothesis, what are the names and the symbols for the two hypotheses we typically generate? | Null hypothesis H0 and the alternative hypothesis H1 |

What is the type error and symbol for the probability we will reject the null hypothesis when it is actually true? | Type I error: α |

What is Type II error β? | The probability we will accept the null hypothesis when the actual population mean is a different value (i.e. the null hypothesis is actually false). |

How is α typically determined? | It is selected by the person conducting the experiment / study. |

Is it possible to determine β for all potential alternative distributions? | We cannot determine β for all potential alternative distributions, because there are an infinite number of alternative distributions. |

Is it possible to determine β is for a particular alternative distribution? | We can determine β for a particular alternative distributions |

What does a P-value represent? | It is the probability, assuming that H 0 (null hypothesis) is true, of obtaining a test (i.e. sample) statistic that is that value or further away from the mean. |

Can a P-value ever be negative? | No a p-value cannot be negative because it represents a probability which cannot be less than 0 |

can a p-value ever be 1? | Yes, a p-value can be 1. When x = μ , the p-value is 1 |

Can a p-value ever be greater than 1? | No, it cannot be greater than 1, because it represents a probability. Probabilities cannot be greater than 1. |

When testing a hypothesis with an unknown standard deviation, what is done? | Same procedures as with known standard dev, but use t value instead of z. |

If P <= α, the result is _______________ ______________ at the α level. | statistically significant |

When P < α do we reject or not reject the null hypothesis? | We reject the null hypothesis If P < α |

When testing a one sided hypothesis we follow same steps as two sided but we dont _______ | divide α by 2. only one rejection region. must determine the direction of the rejection region. |

If samples are taken from two different continuous random variable distributions and the means of those two samples are x1& x2 , then is x1 − x2 a random variable? | Yes |

Is the variance of x2 − x1 bigger or smaller than the variance for x2 or x1 ? | The variance for x2 − x1 would be bigger than either one, provided both x2 or x1 are both greater than 0. |

If we wish to test if the population means from two continuous random variable distributions are equal, then what null and alternative hypotheses should be write? | H0: μ1−μ2=0 |

If we wish to test if the population means from two continuous random variable distributions are a specific difference apart from each other, then what null and alternative hypotheses should be write? | H0: μ1−μ2=d Ha: μ1−μ2≠d where d = the specific difference |

If we wish to compare the population proportions of two binomial random variable distributions, what sample statistics do we use to make the comparison? | pˆ 1 a n d pˆ 2 |

What are the conditions necessary to have a valid large-sample inferences about p1 − p2 ? | ● Both samples are representative of their populations ● The two samples are independent of each other ● np≥10 and n(1 − p)≥10 for both populations / samples ● The two populations are at least 20 times the size of their respective samples |

For 96% confidence, what is the appropriate z-value to use: | α=1−.96=.04; α2 =.02; zα2 =2.055; |

If we wish to test if the population proportions from two binomial random variable distributions are equal, then what null and alternative hypotheses should be write? | H0: p1−p2=0 H1: p1−p2≠0 |

If we don’t know the underlying σ1^2 and σ2^2 for the two continuous random variable distributions, but there is a set of sample data from each distribution, what sample statistics are used to estimate σ1^2 and σ2^2 in the formula for σ(x1−x2) ? | s1^2 & s2^2 |

Created by:
aiur100