1. Allen's hummingbird (Selasphorus sasin) has been studied by zoologist Bill Alther.Suppose a small group of14Allen's hummingbirds has been under study in Arizona. The average weight for these birds isx= 3.15 grams.Based on previous studies, we can assume that the weights of Allen's hummingbirds have a normal distribution, with=0.40gram.

(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

(d) Find the sample size necessary for an 80% confidence level with a maximal margin of errorE=0.11for the mean weights of the hummingbirds. (Round up to the nearest whole number.) hummingbirds

2. 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 eleven blood tests for uric acid. The mean concentration was x = 5.38 mg/dl. The distribution of uric acid in healthy adult males can be assumed to be normal, with = 1.85 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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upper limit=

margin of error=

(d)Find the sample size necessary for a 95% confidence level with maximal margin of error E = 1.14 for the mean concentration of uric acid in this patient's blood. (Round your answer up to the nearest whole number.)

blood tests

3. 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 of50male firefighters are tested and that they have a plasma volume sample mean ofx= 37.5 ml/kg(milliliters plasma per kilogram body weight). Assume that=7.80ml/kgfor 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.)

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upper limit=

margin of error=

(d)Find the sample size necessary for a 99% confidence level with maximal margin of errorE=2.40for the mean plasma volume in male firefighters. (Round up to the nearest whole number.)

male firefighters

4. The method of tree ring dating gave the following years A.D. for an archaeological excavation site. Assume that the population ofxvalues has an approximately normal distribution.

1,222

1,264

1,292

1,243

1,268

1,316

1,275

1,317

1,275

(a) Use a calculator with mean and standard deviation keys to find the sample mean yearxand sample standard deviations. (Round your answers to four decimal places.)

x=	A.D.
s=	yr

(b) Find a 90% confidence interval for the mean of all tree ring dates from this archaeological site. (Round your answers to the nearest whole number.)

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upper limit	A.D.

5. How much does a sleeping bag cost? Let's say you want a sleeping bag that should keep you warm in temperatures from20Fto45F.A random sample of prices ($) for sleeping bags in this temperature range is given below. Assume that the population ofxvalues has an approximately normal distribution.

90	70	105	90	110	55	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 pricexand sample standard deviations. (Round your answers to four decimal places.)

x= $

s= $

(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 priceof all summer sleeping bags. (Round your answers to two decimal places.)

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upper limit = $

6. 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 ofxvalues has an approximately normal distribution.

93

177

130

91

75

94

116

100

85

(a) Use a calculator with mean and sample standard deviation keys to find the sample mean startup costxand sample standard deviations. (Round your answers to four decimal places.)

x=	thousand dollars
s=	thousand dollars

(b) Find a 90% confidence interval for the population average startup costsfor candy store franchises. (Round your answers to one decimal place.)

lower limit	thousand dollars
upper limit	thousand dollars

7. For this problem, carry at least four digits after the decimal in your calculations. Answers may vary slightly due to rounding. In a random sample of65professional actors, it was found that35were extroverts.

(a) Letprepresent the proportion of all actors who are extroverts. Find a point estimate forp. (Round your answer to four decimal places.) (b) Find a 95% confidence interval forp. (Round your answers to two decimal places.)

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8.For this problem, carry at least four digits after the decimal in your calculations. Answers may vary slightly due to rounding.In a random sample of512judges, it was found that281were introverts.

(a)Letprepresent the proportion of all judges who are introverts. Find a point estimate forp. (Round your answer to four decimal places.)

(b)Find a 99% confidence interval forp. (Round your answers to two decimal places.)

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upper limit=

9. Independent random samples of professional football and basketball players gave the following information. Assume that the weight distributions are mound-shaped and symmetric.Weights (in lb) of pro football players:x₁;n₁= 21

249	262	255	251	244	276	240	265	257	252	282
256	250	264	270	275	245	275	253	265	272

Weights (in lb) of pro basketball players:x₂;n₂= 19

202	200	220	210	193	215	221	216	228	207
225	208	195	191	207	196	182	193	201

(a) Use a calculator with mean and standard deviation keys to calculatex₁,s₁,x₂, ands₂. (Round your answers to four decimal places.)

x1=
s1=
x2=
s2=

(b) Let₁be the population mean forx₁and let₂be the population mean forx₂. Find a 99% confidence interval for₁₂.(Round your answers to one decimal place.)

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10. The following data represent petal lengths (in cm) for independent random samples of two species of iris.

5.0	5.6	6.1	6.1	5.1	5.5	5.3	5.5	6.9	5.0	4.9	6.0	4.8	6.1	5.6	5.1
5.6	4.8	5.4	5.1	5.1	5.9	5.2	5.7	5.4	4.5	6.4	5.3	5.5	6.7	5.7	4.9
4.8	5.7	5.1	5.1

1.6	1.6	1.4	1.5	1.5	1.6	1.4	1.1	1.2	1.4	1.7	1.0	1.7	1.9	1.6	1.4
1.5	1.4	1.2	1.3	1.5	1.3	1.6	1.9	1.4	1.6	1.5	1.4	1.6	1.2	1.9	1.5
1.6	1.4	1.3	1.7	1.5	1.5

(a)Use a calculator with mean and standard deviation keys to calculatex₁,s₁,x₂, ands₂. (Round your answers to four decimal places.)

x₁=

s₁=

x₂=

s₂=

(b)Let₁be the population mean forx₁and let₂be the population mean forx₂. Find a 99% confidence interval for₁₂.(Round your answers to two decimal places.)

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upper limit=

11. A random sample of380married couples found that298had two or more personality preferences in common. In another random sample of576married couples, it was found that only38had no preferences in common. Letp₁be the population proportion of all married couples who have two or more personality preferences in common. Letp₂be the population proportion of all married couples who have no personality preferences in common.

(a) Find a95%confidence interval forp₁-p₂. (Use 3 decimal places.)

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12. The U.S. Geological Survey compiled historical data about Old Faithful Geyser (Yellowstone National Park) from 1870 to 1987. Let x₁ be a random variable that represents the time interval (in minutes) between Old Faithful eruptions for the years 1948 to 1952. Based on 9160 observations, the sample mean interval was x₁ = 62.0 minutes. Let x₂ be a random variable that represents the time interval in minutes between Old Faithful eruptions for the years 1983 to 1987. Based on 24,404 observations, the sample mean time interval was x₂ = 70.0 minutes. Historical data suggest that ₁ = 8.77minutes and ₂ = 11.64 minutes. Let ₁ be the population mean of x₁ and let ₂ be the population mean of x₂.(a) Compute a 90% confidence interval for ₁ - ₂. (Use 2 decimal places.)

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