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Thirty-five 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 42.7 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.)
(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.)
(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.)

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zainsubhani

Answer:

Part A:

Error Margin= 11.9

Interval is 126.6 to 150.4

Part B:

Error Margin=14.1

Interval is 124.4 to 152.6

Part C:

Error Margin=18.6

Interval is 119.9 to 157.1

Step-by-step explanation:

Confidence Interval                                Z

90%                                                     1.645

95%                                                     1.96

99%                                                     2.58

Formula used in all three parts:

Error Margin=Z*σ/[tex]\sqrt{n}[/tex]

Upper limit of Interval=x+ Error Margin

Lower limit of Interval=x- Error Margin

Part A:

Error Margin=1.645*42.7/[tex]\sqrt{35}[/tex]

Error Margin= 11.9

Upper limit of Interval=138.5+ 11.9

Upper limit of Interval=150.4

Lower limit of Interval=138.5 - 11.9

Lower limit of Interval=126.6

Interval is 126.6 to 150.4

Part B:

Error Margin=1.96*42.7/[tex]\sqrt{35}[/tex]

Error Margin=14.1

Upper limit of Interval=138.5+ 14.1

Upper limit of Interval=152.6

Lower limit of Interval=138.5 - 14.1

Lower limit of Interval=124.4

Interval is 124.4 to 152.6

Part C:

Error Margin=2.58*42.7/[tex]\sqrt{35}[/tex]

Error Margin=18.6

Upper limit of Interval=138.5+ 18.6

Upper limit of Interval=157.1

Lower limit of Interval=138.5 - 18.6

Lower limit of Interval=119.9

Interval is 119.9 to 157.1

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