Chapter 6, Problem 6.16P

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Textbook Problem

Nation |
Percent“Very happy” |
Sample Size |
Confidence Intreval |

Germany | 21.1% | 2046 | |

Japan | 32.3% | 2443 | |

Chili | 24.4% | 1000 | |

China | 15.7% | 2300 | |

Malaysia | 56.6% | 1300 | |

Nigeria | 55.6% | 1759 | |

Russia | 14.8% | 2200 |

To determine

**To find:**

The confidence interval for the population mean for the specified level.

Explanation

**Given:**

The given information is,

The World Values Survey is administered periodically to random samples from societies around the globe.

The given table of information is,

Nation | Percent “Very happy” |
Sample Size | Confidence Intreval |

Germany | 21.1% | 2046 | |

Japan | 32.3% | 2443 | |

Chili | 24.4% | 1000 | |

China | 15.7% | 2300 | |

Malaysia | 56.6% | 1300 | |

Nigeria | 55.6% | 1759 | |

Russia | 14.8% | 2200 |

**Approach:**

The confidence interval is an interval estimate from the statistics of the observed data that might contain the true value of the unknown population parameter.

**Formula used:**

For large samples and given sample proportion, the confidence interval (*c.i.*) is given by,

Where,

*Z* is the *Z* score determined by the alpha level and,

*N* is the sample size.

**Calculation:**

The level of confidence is 95%.

For 95%, the *Z* value is given as,

For large samples and given sample proportion, the confidence interval (*c.i.*) is given by,

The confidence interval for Germany is given as,

Substitute 0.211 for *Z* and 2046 for

Thus, the 95% confidence interval for Germany is,

The confidence interval for Japan is given as,

Substitute 0.323 for *Z* and 2443 for

Thus, the 95% confidence interval for Japan is,

The confidence interval for Chili is given as,

Substitute 0.244 for *Z* and 1000 for

Thus, the 95% confidence interval for Chili is,

The confidence interval for China is given as,

Substitute 0.157 for *Z* and 2300 for

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