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Z Value for Confidence Level

Z Value for Confidence Level | ||
---|---|---|

Confidence Level | 91 % | 95% |

Z Value | 1.70 | 1.96 |

Confidence Level | z |
---|---|

0.85 | 1.44 |

0.90 | 1.645 |

0.92 | 1.75 |

0.95 | 1.96 |

where Z is the value from the standard normal distribution for the selected confidence level (e.g., for a 95% confidence level, Z =1.96). In practice, we often do not know the value of the population standard deviation (σ). Confidence Intervals.

Desired Confidence Interval | Z Score |
---|---|

90 % 95% 99% | 1.645 1.96 2.576 |

Area in Tails

Confidence Level | Area between 0 and z -score | z -score |
---|---|---|

90% | 0.4500 | 1.645 |

95% | 0.4750 | 1.960 |

98% | 0.4900 | 2.326 |

99 % | 0.4950 | 2.576 |

Thus Z_{α}_{/}_{2} = 1.645 for 90% confidence. 2) Use the t-Distribution table (Table A-3, p. 726). Example: Find Z_{α}_{/}_{2} for 98% confidence.

Confidence (1–α) g 100% | Significance α | Critical Value Z_{α}_{/}_{2} |
---|---|---|

90% | 0.10 | 1.645 |

95% | 0.05 | 1.960 |

98% | 0.02 | 2.326 |

99 % | 0.01 | 2.576 |

Because you want a 95 % confidence interval, your z*-value is 1.96. Suppose you take a random sample of 100 fingerlings and determine that the average length is 7.5 inches; assume the population standard deviation is 2.3 inches. Multiply 1.96 times 2.3 divided by the square root of 100 (which is 10).

B. Common confidence levels and their critical values

Confidence Level | Critical Value ( Z – score ) |
---|---|

0.92 | 1.75 |

0.93 | 1.81 |

0.94 | 1.88 |

0.95 | 1.96 |

Conclusion

Confidence Interval | Z |
---|---|

90% | 1.645 |

95 % | 1.960 |

99% | 2.576 |

99.5% | 2.807 |

A larger sample size or lower variability will result in a tighter confidence interval with a smaller margin of error. A smaller sample size or a higher variability will result in a wider confidence interval with a larger margin of error. A tight interval at 95% or higher confidence is ideal.

The first way to find the p – value is to use the z -table. In the z -table, the left column will show values to the tenths place, while the top row will show values to the hundredths place. If we have a z -score of -1.304, we need to round this to the hundredths place, or -1.30.

Z-values for Confidence Intervals

Confidence Level | Z Value |
---|---|

75 % | 1.150 |

80% | 1.282 |

85% | 1.440 |

90% | 1.645 |

There are four steps to constructing a confidence interval. Identify a sample statistic. Choose the statistic (e.g, sample mean, sample proportion) that you will use to estimate a population parameter. Select a confidence level. Find the margin of error. Specify the confidence interval.

How to Find a Confidence Interval for a Proportion: Steps α: subtract the given CI from 1. 1-.9=.10. z _{α}_{/}_{2}: divide α by 2, then look up that area in the z-table. : Divide the proportion given (i.e. the smaller number)by the sample size. : To find q-hat, subtract p-hat (from directly above) from 1.

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