9.)
Overproduction of uric acid in the body can be an indication of cell
eakdown. 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 seven 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 e
or? (Round your answers to two decimal places.)
lower limit
1
upper limit
2
margin of e
or
3
(b) What conditions are necessary for your calculations? (Select all that apply.)
σ is unknownnormal distribution of uric acidn is largeσ is knownuniform distribution of uric acid
(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. There is not enough information to make an interpretation. There is a 95% chance that the confidence interval is one of the intervals containing the population average uric acid level for this patient. The probability that this interval contains the true average uric acid level for this patient is 0.05. There is a 5% chance that the confidence interval is one of the intervals containing the population average uric acid level for this patient.
(d) Find the sample size necessary for a 95% confidence level with maximal margin of e
or E = 1.16 for the mean concentration of uric acid in this patient's blood. (Round your answer up to the nearest whole number.)
6 blood tests
10.)
What price do farmers get for their watermelon crops? In the third week of July, a random sample of 43 farming regions gave a sample mean of x = $6.88 per 100 pounds of watermelon. Assume that σ is known to be $1.92 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 e
or? (Round your answers to two decimal places.)
lower limit
$ 1
upper limit
$ 2
margin of e
or
$ 3
(b) Find the sample size necessary for a 90% confidence level with maximal e
or of estimate E = 0.39 for the mean price per 100 pounds of watermelon. (Round up to the nearest whole number.)
4 farming regions
(c) A farm
ings 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 e
or? Hint: 1 ton is 2000 pounds. (Round your answers to two decimal places.)
lower limit
$ 5
upper limit
$ 6
margin of e
or
$ 7
11.)
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 σ is known to be 43.7 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 e
or? (Round your answers to one decimal place.)
lower limit
1
upper limit
2
margin of e
or
3
(b) Find a 95% confidence interval for the population mean annual number of reported larceny cases in such communities. What is the margin of e
or? (Round your answers to one decimal place.)
lower limit
4
upper limit
5
margin of e
or
6
(c) Find a 99% confidence interval for the population mean annual number of reported larceny cases in such communities. What is the margin of e
or? (Round your answers to one decimal place.)
lower limit
7
upper limit
8
margin of e
or
9
14.)
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.
115
50
55
55
120
85
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 =
$ 1
s =
$ 2
(b) Using the given data as representative of the population of prices of all summer sleeping bags, find a 90% confidence interval for the mean price μ of all summer sleeping bags. (Round your answers to two decimal places.)
lower limit
$ 3
upper limit
$ 4
15.)
Do you want to own your own candy store? Wow! With some interest in running your own business and a decent credit rating, you can probably get a bank loan on startup costs for franchises such as Candy Express, The Fudge Company, Karmel Corn, and Rocky Mountain Chocolate Factory. Startup costs (in thousands of dollars) for a random sample of candy stores are given below. Assume that the population of x values has an approximately normal distribution.
93
180
134
91
75
94
116
100
85
(a) Use a calculator with mean and sample standard deviation keys to find the sample mean startup cost x and sample standard deviation s. (Round your answers to one decimal place.)
x =
1 thousand dollars
s =
2 thousand dollars
(b) Find a 90% confidence interval for the population average startup costs μ for candy store franchises. (Round your answers to one decimal place.)
lower limit
3 thousand dollars
upper limit
4 thousand dollars
16.)
Over the past several months, an adult patient has been treated for tetany (severe muscle spasms). This condition is associated with an average total calcium level below 6 mg/dl. Recently, the patient's total calcium tests gave the following readings (in mg/dl). Assume that the population of x values has an approximately normal distribution.
9.9
8.6
10.1
9.3
9.4
9.8
10.0
9.9
11.2
12.1
(a) Use a calculator with mean and sample standard deviation keys to find the sample mean reading x and the sample standard deviation s. (Round your answers to two decimal places.)
x =
1 mg/dl
s =
2 mg/dl
(b) Find a 99.9% confidence interval for the population mean of total calcium in this patient's blood. (Round your answer to two decimal places.)
lower limit
3 mg/dl
upper limit
4 mg/dl
17.)
What percentage of hospitals provide at least some charity care? Based on a random sample of hospital reports from eastern states, the following information is obtained (units in percentage of hospitals providing at least some charity care):
57.5
56.2
53.1
65.7
59.0
64.7
70.1
64.7
53.5
78.2
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 percentage x and the sample standard deviation s. (Round your answers to one decimal place.)
x =
1 %
s =
2 %
(b) Find a 90% confidence interval for the population average μ of the percentage of hospitals providing at least some charity care. (Round your answers to one decimal place.)
lower limit
3 %
upper limit
4 %
19.)
For this problem, ca
y at least four digits after the decimal in your calculations. Answers may vary slightly due to rounding.
In a random sample of 67 professional actors, it was found that 40 were extroverts.
(a) Let p represent the proportion of all actors who are extroverts. Find a point estimate for p. (Round your answer to four decimal places.)
1
(b) Find a 95% confidence interval for p. (Round your answers to two decimal places.)
lower limit
2
upper limit
3
20.)
For this problem, ca
y at least four digits after the decimal in your calculations. Answers may vary slightly due to rounding.
A random sample of 5994 physicians in Colorado showed that 3008 provided at least some charity care (i.e., treated poor people at no cost).
(a) Let p represent the proportion of all Colorado physicians who provide some charity care. Find a point estimate for p. (Round your answer to four decimal places.)
1
(b) Find a 99% confidence interval for p. (Round your answers to three decimal places.)
lower limit
2
upper limit
3
21.)
For this problem, ca
y at least four digits after the decimal in your calculations. Answers may vary slightly due to rounding.
Case studies showed that out of 10,103 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.)
1
(b) Find a 99% confidence interval for p. (Round your answers to three decimal places.)
lower limit
2
upper limit
3
22.)
For this problem, ca
y 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 38 out of 833 fish died when caught and released using ba
less 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 ba
less hooks. Find a point estimate for p. (Round your answer to four decimal places.)
1
(b) Find a 99% confidence interval for p. (Round your answers to three decimal places.)
lower limit
2
upper limit
3
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