Question

Thirty-one 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 45.1
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 |

(d) Compare the margins of error for parts (a) through (c). As the
confidence levels increase, do the margins of error increase?

As the confidence level increases, the margin of error decreases.As the confidence level increases, the margin of error increases. As the confidence level increases, the margin of error remains the same.

(e) Compare the lengths of the confidence intervals for parts (a)
through (c). As the confidence levels increase, do the confidence
intervals increase in length?

As the confidence level increases, the confidence interval decreases in length.As the confidence level increases, the confidence interval remains the same length. As the confidence level increases, the confidence interval increases in length.

Answer #1

Ans:

a)

Margin of error=1.645*(45.1/sqrt(31))=**13.3**

lower limit=138.5-13.3=**125.2**

upper limit=138.5+13.3**=151.8**

b)

Margin of error=1.96*(45.1/SQRT(31))=**15.9**

lower limit=138.5-15.9=**122.6**

upper limit=138.5+15.9**=154.4**

c)

Margin of error=2.576*(45.1/SQRT(31))=**20.9**

lower limit=138.5-20.9=**117.6**

upper limit=138.5+20.9**=159.4**

d)

As the confidence level **increases, the margin of error
increases. **

e)

As the confidence level **increases,**
the confidence interval **increases in length.**

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reported larceny cases in such communities. What is the margin of
error? (Round your answers to one decimal place.)
lower limit
upper limit
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annual number of reported larceny cases in such communities. What
is the margin of error? (Round your answers to one decimal place.)
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annual number of reported larceny cases in such communities. What
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