Thirty-two small communities in Connecticut (population near10,000 each) gave an average of x = 138.5 reported casesof larceny per year. Assume that σ is known to be 44.9cases per year.

(a) Find a 90% confidence interval for the population meanannual number of reported larceny cases in such communities. Whatis the margin of error? (Round your answers to one decimalplace.)

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upper limit   Â
margin of error   Â

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

lower limit   Â
upper limit   Â
margin of error   Â

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

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upper limit   Â
margin of error   Â

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

As the confidence level increases, the margin of error remainsthe same.As the confidence level increases, the margin of errordecreases.     As the confidence levelincreases, the margin of error increases.

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

As the confidence level increases, the confidence intervalincreases in length.As the confidence level increases, theconfidence interval remains the samelength.     As the confidence levelincreases, the confidence interval decreases in length.

Allen's hummingbird (Selasphorus sasin) has beenstudied by zoologist Bill Alther.† Suppose a small group of 15Allen's hummingbirds has been under study in Arizona. The averageweight for these birds is x = 3.15 grams. Based onprevious studies, we can assume that the weights of Allen'shummingbirds have a normal distribution, with σ = 0.22gram.

When finding an 80% confidence interval, what is the criticalvalue for confidence level? (Give your answer to two decimalplaces.)

z_c =

(a)

Find an 80% confidence interval for the average weights ofAllen's hummingbirds in the study region. What is the margin oferror? (Round your answers to two decimal places.)

lower limitupper limitmargin of error

(b)

What conditions are necessary for your calculations? (Select allthat apply.)

normal distribution of weightsuniform distribution ofweightsσ is knownσ is unknownn islarge

(c)

Interpret your results in the context of this problem.

The probability that this interval contains the true averageweight of Allen's hummingbirds is 0.80.There is a 20% chance thatthe interval is one of the intervals containing the true averageweight of Allen's hummingbirds in thisregion.     There is an 80% chance thatthe interval is one of the intervals containing the true averageweight of Allen's hummingbirds in this region.The probability thatthis interval contains the true average weight of Allen'shummingbirds is 0.20.The probability to the true average weight ofAllen's hummingbirds is equal to the sample mean.

(d)

Which equation is used to find the sample size n forestimating μ when σ is known?

n =

zσ σ

E

	2

n =

zσ E

σ

	2

     n =

zσ E σ

n =

zσ σ E

Find the sample size necessary for an 80% confidence level witha maximal margin of error  E = 0.08 for the meanweights of the hummingbirds. (Round up to the nearest wholenumber.)

hummingbirds