Question

Thirty-two 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 44.9 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 remains the same.As the confidence level increases, the margin of error decreases.     As the confidence level increases, 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 confidence intervals increase in length?

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

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

When finding an 80% confidence interval, what is the critical value for confidence level? (Give your answer to two decimal places.)

z_c =

(a)

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

lower limitupper limitmargin of error

(b)

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

normal distribution of weightsuniform distribution of weightsσ is knownσ is unknownn is large

(c)

Interpret your results in the context of this problem.

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

(d)

Which equation is used to find the sample size n for estimating 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 with a maximal margin of error  E = 0.08 for the mean weights of the hummingbirds. (Round up to the nearest whole number.)

hummingbirds

Answer 1