Q:1

Allen's hummingbird (Selasphorus sasin) has been studied by zoologist Bill Alther.Suppose a small group of19Allen'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=0.22gram.(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?

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

uniform distribution of weights

is unknown

nis large

normal distribution of weights

is known

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

The probability that this interval contains the true average weight of Allen's hummingbirds is 0.80.

We are 80% confident that the true average weight of Allen's hummingbirds falls within this interval.

The probability that this interval contains the true average weight of Allen's hummingbirds is 0.20.

We are 20% confident that the true average weight of Allen's hummingbirds falls within this interval.

Q2

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 takenfifteenblood tests for uric acid. The mean concentration wasx=5.26mg/dl.The distribution of uric acid in healthy adult males can be assumed to be normal, with=1.91mg/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.)

normal distribution of uric acid

is known

uniform distribution of uric acid

nis large

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 0.05.

We are 5% confident that the true uric acid level for this patient falls within this interval.

The probability that this interval contains the true average uric acid level for this patient is 0.95.

We are 95% 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 errorE=1.14for the mean concentration of uric acid in this patient's blood. (Round your answer up to the nearest whole number.)

? blood tests

Q3

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 of44male 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=7.00ml/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.)

lower limit

upper limit

margin of error

(b)

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

the distribution of volumes is uniform

is unknown

the distribution of volumes is normal

is known

nis large

(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 errorE=2.60for the mean plasma volume in male firefighters. (Round up to the nearest whole number.)

? male firefighters

Q4: 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.

1,208 1,229 1,257 1,320 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.)

lower limitA.D.

upper limitA.D.

Q5How 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.

80 50 80 50 115 110 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.)

lower limit$

upper limit$

Q6

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.

92 175 128 97 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 limitthousand dollars

upper limitthousand dollars