Question

Thirty small communities in Connecticut (population near 10,000
each) gave an average of *x* = 138.5 reported cases of
larceny per year. Assume that *σ* is known to be 40.3 cases
per year.

(a) Find a 90% confidence interval for the population mean annual number of reported larceny cases in such communities. What is the margin of error? (Round your answers to one decimal place.)

lower limit | |

upper limit | |

margin of error |

(b) Find a 95% confidence interval for the population mean annual
number of reported larceny cases in such communities. What is the
margin of error? (Round your answers to one decimal place.)

lower limit | |

upper limit | |

margin of error |

(c) Find a 99% confidence interval for the population mean annual
number of reported larceny cases in such communities. What is the
margin of error? (Round your answers to one decimal place.)

lower limit | |

upper limit | |

margin of error |

Answer #1

Formula

Confidence Interval for population Mean When Population Standard deviation is known

Margin of error:

Given,

Sample average reported cases of larceny per year : Sample average : = 138.5

Population Standard deviation : = 40.3 cases per year

Sample Size : n= 30

(a)

for 90% confidence level = (100-90)/100 = 0.1

/2 = 0.05

Z_{/2}
= Z_{0.05} = 1.6449

90% confidence interval for the population mean annual number of reported larceny cases in such communities

Margin of error

lower limit | 126.4 |

upper limit | 150.6 |

margin of error | 12.1 |

(b)

for 95% confidence level = (100-95)/100 = 0.05

/2 = 0.025

Z_{/2}
= Z_{0.025} = 1.96

95% confidence interval for the population mean annual number of reported larceny cases in such communities

Margin of error :

lower limit | 124.1 |

upper limit | 152.9 |

margin of error | 14.4 |

(c)

for 99% confidence level = (100-99)/100 = 0.01

/2 = 0.005

Z_{/2}
= Z_{0.005} = 2.5758

99% confidence interval for the population mean annual number of reported larceny cases in such communities

Margin of error:

lower limit | 119.5 |

upper limit | 157.5 |

margin of error | 19.0 |

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