Thirty-one small communities in Connecticut (population near 10,000 each) gave a

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 is known to be 40.9cases 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.)

(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 increases 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.

2)How much do wild mountain lions weigh? Adult wild mountain lions (18 months or older) captured and released for the first time in the San Andres Mountains gave the following weights (pounds):

Assume that the population of x values has an approximately normal distribution.(a) Use a calculator with mean and sample standard deviation keys to find the sample mean weight x and sample standard deviation s. (Round your answers to one decimal place.)

(b) Find a 75% confidence interval for the population average weight of all adult mountain lions in the specified region. (Round your answers to one decimal place.)

lower limit     upper limit     margin of error    

Explanation / Answer

as population std deviation is known, we will use z distribution

std error of mean =std deviation/(n)1/2 =7.346

for 90% CI, z=1.645

hence lower limit =sample mean -z*std error =126.4171

upper limit =sample mean +z*std error =150.5829

margin of error =z*std error =12.0829

b)

std error of mean =std deviation/(n)1/2 =7.346

for 95% CI, z=1.96

hence lower limit =sample mean -z*std error =124.1024

upper limit =sample mean +z*std error =152.8976

margin of error =z*std error =14.3976

c)

std error of mean =std deviation/(n)1/2 =7.346

for 99% CI, z=2.5758

hence lower limit =sample mean -z*std error =119.5783

upper limit =sample mean +z*std error =157.4217

margin of error =z*std error =18.9217

d).As the confidence level increases, the margin of error increases

e)As the confidence level increases, the confidence interval increases in length

2)as we do not knoe std deviation of population ; we will use student t distribution here.

from above x=92.833

std deviation =31.096

b) for 75%; and 5 degree of freedom t=1.3009

hence lower limit =sample mean -t*std error =76.3179

upper limit =sample mean +t*std error =109.3488

X 75 102 133 123 60 64 mean(X) 92.833 std deviation(S) 31.096 std error =S/(n)1/2 12.6949

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