For this problem, carry at least four digits after the decimal in your calculations. Answers may vary slightly due to rounding.Case studies showed that out of 10,001 convicts who escaped from certain prisons, only 7535 were recaptured.
(a) Let p represent the proportion of all escaped convicts who will eventually be recaptured. Find a point estimate for p. (Round your answer to four decimal places.)(b) Find a 99% confidence interval for p. (Round your answers to three decimal places.)
lower limit
upper limitGive a brief statement of the meaning of the confidence interval.
1% of the confidence intervals created using this method would include the true proportion of recaptured escaped convicts.
99% of all confidence intervals would include the true proportion of recaptured escaped convicts.
99% of the confidence intervals created using this method would include the true proportion of recaptured escaped convicts.
For this problem, carry at least four digits after the decimal in your calculations. Answers may vary slightly due to rounding.In a combined study of northern pike, cutthroat trout, rainbow trout, and lake trout, it was found that 32 out of 815 fish died when caught and released using barbless hooks on flies or lures. All hooks were removed from the fish.
(a) Let p represent the proportion of all pike and trout that die (i.e., p is the mortality rate) when caught and released using barbless hooks. Find a point estimate for p. (Round your answer to four decimal places.)(b) Find a 99% confidence interval for p. (Round your answers to three decimal places.)
lower limit
upper limitGive a brief explanation of the meaning of the interval.
99% of the confidence intervals created using this method would include the true catch-and-release mortality rate.
1% of the confidence intervals created using this method would include the true catch-and-release mortality rate.
A random sample of 326 medical doctors showed that 176 had a solo practice.
(a) Let p represent the proportion of all medical doctors who have a solo practice. Find a point estimate for p. (Use 3 decimal places.)(b) Find a 98% confidence interval for p. (Use 3 decimal places.)
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upper limit
Give a brief explanation of the meaning of the interval.
98% of the confidence intervals created using this method would include the true proportion of physicians with solo practices.
2% of the all confidence intervals would include the true proportion of physicians with solo practices.
2% of the confidence intervals created using this method would include the true proportion of physicians with solo practices.
98% of the all confidence intervals would include the true proportion of physicians with solo practices.(c) As a news writer, how would you report the survey results regarding the percentage of medical doctors in solo practice?
How much does a sleeping bag cost? Let's say you want a sleeping bag that should keep you warm in temperatures from 20°F to 45°F. A random sample of prices ($) for sleeping bags in this temperature range is given below. Assume that the population of x values has an approximately normal distribution.
95 115 100 95 50 105 30 23 100 110
105 95 105 60 110 120 95 90 60 70
(a) Use a calculator with mean and sample standard deviation keys to find the sample mean price x and sample standard deviation s. (Round your answers to two decimal places.)
x = $
Let x be a random variable that represents white blood cell count per cubic milliliter of whole blood. Assume that x has a distribution that is approximately normal, with mean μ = 7150 and estimated standard deviation σ = 2200. A test result of x < 3500 is an indication of leukopenia. This indicates bone marrow depression that may be the result of a viral infection.
(a) What is the probability that, on a single test, x is less than 3500? (Round your answer to four decimal places.)(b) Suppose a doctor uses the average x for two tests taken about a week apart. What can we say about the probability distribution of x?
The probability distribution of x is approximately normal with μx = 7150 and σx = 2200.
The probability distribution of x is not normal.
The probability distribution of x is approximately normal with μx = 7150 and σx = 1555.63.
The probability distribution of x is approximately normal with μx = 7150 and σx = 1100.00.What is the probability of x < 3500? (Round your answer to four decimal places.)(c) Repeat part (b) for n = 3 tests taken a week apart. (Round your answer to four decimal places.)(d) Compare your answers to parts (a), (b), and (c). How did the probabilities change as n increased?
Let x be a random variable that represents the weights in kilograms (kg) of healthy adult female deer (does) in December in a national park. Then x has a distribution that is approximately normal with mean μ = 51.0 kg and standard deviation σ = 8.1 kg. Suppose a doe that weighs less than 42 kg is considered undernourished.
(a) What is the probability that a single doe captured (weighed and released) at random in December is undernourished? (Round your answer to four decimal places.)(b) If the park has about 2850 does, what number do you expect to be undernourished in December? (Round your answer to the nearest whole number.)
does(c) To estimate the health of the December doe population, park rangers use the rule that the average weight of n = 50 does should be more than 48 kg. If the average weight is less than 48 kg, it is thought that the entire population of does might be undernourished. What is the probability that the average weight
Allen's hummingbird (Selasphorus sasin) has been studied by zoologist Bill Alther.† Suppose a small group of 16 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 = 0.38 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.)
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margin of error(b) What conditions are necessary for your calculations? (Select all that apply.)
σ is known
normal distribution of weights
uniform distribution of weights
n is large
σ is unknown(c) Interpret your results in the context of this problem.
The probability to the true average weight of Allen's hummingbirds is equal to the sample mean.
The probability that this interval contains the true average weight of Allen's hummingbirds is 0.20.
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.
The probability that this interval contains the true average weight of Allen's hummingbirds is 0.80.
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.(d) Find the sample size necessary for an 80% confidence level with a maximal margin of error E = 0.09 for the mean weights of the hummingbirds. (Round up to the nearest whole number.)
hummingbirds
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 six 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 = 1.75 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.)
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margin of error(b) What conditions are necessary for your calculations? (Select all that apply.)
σ is unknown
n is large
σ is known
uniform distribution of uric acid
normal distribution of uric acid(c) Interpret your results in the context of this problem.
What price do farmers get for their watermelon crops? In the third week of July, a random sample of 42 farming regions gave a sample mean of x = $6.88 per 100 pounds of watermelon. Assume that σ is known to be $1.96 per 100 pounds.
(a) Find a 90% confidence interval for the population mean price (per 100 pounds) that farmers in this region get for their watermelon crop. What is the margin of error? (Round your answers to two decimal places.)
lower limit $
upper limit $
margin of error $(b) Find the sample size necessary for a 90% confidence level with maximal error of estimate E = 0.27 for the mean price per 100 pounds of watermelon. (Round up to the nearest whole number.)
farming regions(c) A farm brings 15 tons of watermelon to market. Find a 90% confidence interval for the population mean cash value of this crop. What is the margin of error? Hint: 1 ton is 2000 pounds. (Round your answers to two decimal places.)
lower limit $
upper limit $
margin of error $
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 σ is known to be 42.1 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.)
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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.)
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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.)
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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 increases.
As the confidence level increases, the margin of error decreases.(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 decreases in length.
As the confidence level increases, the confidence interval remains the same length.
As the confidence level increases, the confidence interval increases in length.
a) Lower limit = 126.8
Suppose x has a distribution with a mean of 90 and a standard deviation of 21. Random samples of size
n = 36
are drawn.
(a) Describe the
x distribution
and compute the mean and standard deviation of the distribution.
x
has distribution with
mean μx =
and
standard deviation σx = .(b) Find the z value corresponding to
x = 83.
z =(c) Find
P(x < 83).
(Round your answer to four decimal places.)
P(x < 83) =(d) Would it be unusual for a random sample of size 36 from the x distribution to have a sample mean less than 83? Explain.
6 years ago
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