Question Part Points Submissions Used Thirty-five small communities in Connectic
ID: 3154955 • Letter: Q
Question
Question Part Points Submissions Used 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 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
Explanation / Answer
a)
Note that
Margin of Error E = z(alpha/2) * s / sqrt(n)
Lower Bound = X - z(alpha/2) * s / sqrt(n)
Upper Bound = X + z(alpha/2) * s / sqrt(n)
where
alpha/2 = (1 - confidence level)/2 = 0.05
X = sample mean = 138.5
z(alpha/2) = critical z for the confidence interval = 1.644853627
s = sample standard deviation = 45.1
n = sample size = 35
Thus,
Lower bound = 125.9608015
Upper bound = 151.0391985
Margin of Error E = 12.53919847 [ANSWER]
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b)
Note that
Margin of Error E = z(alpha/2) * s / sqrt(n)
Lower Bound = X - z(alpha/2) * s / sqrt(n)
Upper Bound = X + z(alpha/2) * s / sqrt(n)
where
alpha/2 = (1 - confidence level)/2 = 0.025
X = sample mean = 138.5
z(alpha/2) = critical z for the confidence interval = 1.959963985
s = sample standard deviation = 45.1
n = sample size = 35
Thus,
Lower bound = 123.5586235
Upper bound = 153.4413765
Margin of Error E = 14.94137654 [ANSWER]
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c)
Note that
Margin of Error E = z(alpha/2) * s / sqrt(n)
Lower Bound = X - z(alpha/2) * s / sqrt(n)
Upper Bound = X + z(alpha/2) * s / sqrt(n)
where
alpha/2 = (1 - confidence level)/2 = 0.005
X = sample mean = 138.5
z(alpha/2) = critical z for the confidence interval = 2.575829304
s = sample standard deviation = 45.1
n = sample size = 35
Thus,
Lower bound = 118.8637027
Upper bound = 158.1362973
Margin of Error E = 19.63629732 [ANSWER]
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