Question

Thirty 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 43.7cases 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

Total plasma volume is important in determining the required plasma component in blood replacement therapy for a person undergoing surgery. Plasma volume is influenced by the overall health and physical activity of an individual. Suppose that a random sample of 50 male firefighters are tested and that they have a plasma volume sample mean of x = 37.5 ml/kg (milliliters plasma per kilogram body weight). Assume that σ = 7.30 ml/kg for the distribution of blood plasma.

(a) Find a 99% confidence interval for the population mean blood plasma volume in male firefighters. What is the margin of error? (Round your answers to two decimal places.)

lower limit
upper limit
margin of error

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

σ is knownσ is unknownn is largethe distribution of weights is normalthe distribution of weights is uniform

(c) Interpret your results in the context of this problem.

The probability that this interval contains the true average blood plasma volume in male firefighters is 0.01.The probability that this interval contains the true average blood plasma volume in male firefighters is 0.99.     We are 99% confident that the true average blood plasma volume in male firefighters falls within this interval.We are 1% confident that the true average blood plasma volume in male firefighters falls within this interval.

(d) Find the sample size necessary for a 99% confidence level with maximal margin of error E = 2.30 for the mean plasma volume in male firefighters. (Round up to the nearest whole number.)
male firefighters

Overproduction of uric acid in the body can be an indication of cell breakdown. This may be an advance indication of illness such as gout, leukemia, or lymphoma.† Over a period of months, an adult male patient has taken ten blood tests for uric acid. The mean concentration was x = 5.35 mg/dl. The distribution of uric acid in healthy adult males can be assumed to be normal, with σ = 1.93 mg/dl.

(a) Find a 95% confidence interval for the population mean concentration of uric acid in this patient's blood. What is the margin of error? (Round your answers to two decimal places.)

lower limit
upper limit
margin of error

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

uniform distribution of uric acidn is largeσ is knownnormal distribution of uric acidσ is unknown

(c) Interpret your results in the context of this problem.

The probability that this interval contains the true average uric acid level for this patient is 0.95.The probability that this interval contains the true average uric acid level for this patient is 0.05.     We are 95% confident that the true uric acid level for this patient falls within this interval.We are 5% confident that the true uric acid level for this patient falls within this interval.

(d) Find the sample size necessary for a 95% confidence level with maximal margin of error E = 1.06 for the mean concentration of uric acid in this patient's blood. (Round your answer up to the nearest whole number.)
blood tests

Allen's hummingbird (Selasphorus sasin) has been studied by zoologist Bill Alther.† Suppose a small group of 14 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 = 0.36 gram.

(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 limit
upper limit
margin of error

Answer 1

Solution:- Given that x = 138.5, σ = 43.7, n = 30
90% Confidence interval for Z = 1.645
95% Confidence interval for Z = 1.96
99% Confidence interval for Z = 2.576

(a) 90% Confidence interval for the population mean = X +/- Z*σ/sqrt(n)
= 138.5 +/- 1.645*43.7/sqrt(30)
= 138.5 +/- 13.1
= (125.4

Lower limit = 125.4
upper limit = 151.6
Margin of error = 13.1

(b) 95% Confidence interval for the population mean = X +/- Z*σ/sqrt(n)
= 138.5 +/- 1.96*43.7/sqrt(30)
= 138.5 +/- 15.6
= (122.9 , 154.1)
Lower limit = 122.9
upper limit = 154.1
Margin of error = 15.6

(c) 99% Confidence interval for the population mean = X +/- Z*σ/sqrt(n)
= 138.5 +/- 2.576*43.7/sqrt(30)
= 138.5 +/- 20.6
= (117.9 , 159.1)
Lower limit = 117.9
upper limit = 159.1
Margin of error = 20.6

Note : as the rule only one sum ....