Question

 

Allen's hummingbird (Selasphorus sasin) has been studied by zoologist Bill Alther.† Suppose a small group of 19 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 = 0.22 gram.

Find the sample size necessary for an 80% confidence level with a maximal margin of error E = 0.07 for the mean weights of the hummingbirds. (Round up to the nearest whole number.)

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 43 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 = 7.70 ml/kg for the distribution of blood plasma.

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

σ is knownthe distribution of weights is uniformn is largeσ is unknownthe distribution of weights is normal

(d) Find the sample size necessary for a 99% confidence level with maximal margin of error E = 2.10 for the mean plasma volume in male firefighters. (Round up to the nearest whole number.)

What are the degrees of freedom for Student's t distribution when the sample size is 16?

d.f. =

Use the Student's t distribution to find t_c for a 0.95 confidence level when the sample is 16. (Round your answer to three decimal places.)

Use the Student's t distribution to find t_c for a 0.99 confidence level when the sample is 25. (Round your answer to three decimal places.)

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.

90

175

131

100

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 =	thousand dollars
s =	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	thousand dollars
upper limit	thousand dollars

How much do wild mountain lions weigh? Adult wild mountain lions (18 months or older) captured and released for the first time in the San Andres Mountains gave the following weights (pounds):

66

107

129

126

60

64

Assume that the population of x values has an approximately normal distribution.

(b) Find a 75% confidence interval for the population average weight μ of all adult mountain lions in the specified region. (Round your answers to one decimal place.)

lower limit	lb
upper limit	lb

What is the minimal sample size needed for a 95% confidence interval to have a maximal margin of error of 0.1 in the following scenarios? (Round your answers up the nearest whole number.)

(a) a preliminary estimate for p is 0.17


(b) there is no preliminary estimate for p

For this problem, carry at least four digits after the decimal in your calculations. Answers may vary slightly due to rounding.

A random sample of 5,320 permanent dwellings on an entire reservation showed that 1,662 were traditional hogans.

(a)

Let p be the proportion of all permanent dwellings on the entire reservation that are traditional hogans. Find a point estimate for p. (Round your answer to four decimal places.)

(b)

Find a 99% confidence interval for p. (Round your answer to three decimal places.)

lower limitupper limit

Give a brief interpretation of the confidence interval.

1% of all confidence intervals would include the true proportion of traditional hogans.1% of the confidence intervals created using this method would include the true proportion of traditional hogans.    99% of the confidence intervals created using this method would include the true proportion of traditional hogans.99% of all confidence intervals would include the true proportion of traditional hogans.

(c)

Do you think that np > 5 and nq > 5 are satisfied for this problem? Explain why this would be an important consideration.

No, the conditions are not satisfied. This is important because it allows us to say that p̂ is approximately normal.Yes, the conditions are satisfied. This is important because it allows us to say that p̂ is approximately binomial.    No, the conditions are not satisfied. This is important because it allows us to say that p̂ is approximately binomial.Yes, the conditions are satisfied. This is important because it allows us to say that p̂ is approximately normal.

For this problem, carry at least four digits after the decimal in your calculations. Answers may vary slightly due to rounding.

A random sample of medical files is used to estimate the proportion p of all people who have blood type B.

(a) If you have no preliminary estimate for p, how many medical files should you include in a random sample in order to be 85% sure that the point estimate p̂ will be within a distance of 0.06 from p? (Round your answer up to the nearest whole number.)
medical files

(b) Answer part (a) if you use the preliminary estimate that about 9 out of 90 people have blood type B.
medical files

Answer 1

Allen's hummingbird (Selasphorus sasin) has been studied by zoologist Bill Alther.† Suppose a small group of 19 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 = 0.22 gram.

Find the sample size necessary for an 80% confidence level with a maximal margin of error E = 0.07 for the mean weights of the hummingbirds. (Round up to the nearest whole number.)

z crit for80%=1.281551566

n=(Z*sigma/E)^2

=(1.281551566*0.22/0.07)^2

= 16.22264

n=17(rounded to nearets integer)

sample size,n=17

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 43 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 = 7.70 ml/kg for the distribution of blood plasma.

sigma known and n is large

sample follows normal distribution

σ is known

the distribution of weights is normal

(d) Find the sample size necessary for a 99% confidence level with maximal margin of error E = 2.10 for the mean plasma volume in male firefighters. (Round up to the nearest whole number.)

z crit for 99%=2.576

n=(Z*sigma/MOE)^2

=(2.576*7.70/2.10)^2

= 89.21432

n=90(rounded to nearest integer)

Required sample szie,n=90

What are the degrees of freedom for Student's t distribution when the sample size is 16?

d.f. =n-1=16-1=15

Use the Student's t distribution to find tc for a 0.95 confidence level when the sample is 16. (Round your answer to three decimal places.)

df=n-1=16-1=15

alpha=0.05

alpha/2=0.05/2=0.025

tcritical in excel

==T.INV(0.025,15)

=2.131449546

tc=2.131

Use the Student's t distribution to find tc for a 0.99 confidence level when the sample is 25. (Round your answer to three decimal places.)

alpha=1-0.99=0.01

alpha/2=0.01/2=0.005

df=n-1=25-1=24

critical in excel

==T.INV(0.005,24)

=2.796939505

tc=2.797