Question

1) 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 47 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 = 7.20 ml/kg for 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

(d) Find the sample size necessary for a 99% confidence level with maximal margin of error E = 2.20 for the mean plasma volume in male firefighters. (Round up to the nearest whole number.)

2) The following data represent crime rates per 1000 population for a random sample of 46 Denver neighborhoods.†

63.2	36.3	26.2	53.2	65.3	32.0	65.0
66.3	68.9	35.2	25.1	32.5	54.0	42.4
77.5	123.2	66.3	92.7	56.9	77.1	27.5
69.2	73.8	71.5	58.5	67.2	78.6	33.2
74.9	45.1	132.1	104.7	63.2	59.6	75.7
39.2	69.9	87.5	56.0	154.2	85.5	77.5
84.7	24.2	37.5	41.1

(a) Use a calculator with mean and sample standard deviation keys to find the sample mean x and sample standard deviation s. (Round your answers to one decimal place.)

x =	crimes per 1000 people
s =	crimes per 1000 people

(b) Let us say the preceding data are representative of the population crime rates in Denver neighborhoods. Compute an 80% confidence interval for μ, the population mean crime rate for all Denver neighborhoods. (Round your answers to one decimal place.)

lower limit	crimes per 1000 people
upper limit	crimes per 1000 people

(e) Compute a 95% confidence interval for μ, the population mean crime rate for all Denver neighborhoods. (Round your answers to one decimal place.)

lower limit	crimes per 1000 people
upper limit	crimes per 1000 people

3) 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 of 65 professional actors, it was found that 36 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.)


(b) Find a 95% confidence interval for p. (Round your answers to two decimal places.)

lower limit
upper limit

4) Jobs and productivity! How do banks rate? One way to answer this question is to examine annual profits per employee. The following is data about annual profits per employee (in units of one thousand dollars per employee) for representative companies in financial services. Assume σ ≈ 10.8 thousand dollars.

28.5	27.1	40.4	44.6	28.5	45.3	49.5	32.7	42.5	33.0	33.6
36.9	27.0	47.1	33.8	28.1	28.5	29.1	36.5	36.1	26.9	27.8
28.8	29.3	31.5	31.7	31.1	38.0	32.0	31.7	32.9	23.1	54.9
43.8	36.9	31.9	25.5	23.2	29.8	22.3	26.5	26.7

(a) Use a calculator or appropriate computer software to find x for the preceding data. (Round your answer to two decimal places.)
thousand dollars

(b) Let us say that the preceding data are representative of the entire sector of (successful) financial services corporations. Find a 75% confidence interval for μ, the average annual profit per employee for all successful banks. (Round your answers to two decimal places.)

lower limit	thousand dollars
upper limit	thousand dollars

(e) Find a 90% confidence interval for μ, the average annual profit per employee for all successful banks. (Round your answers to two decimal places.)

lower limit	thousand dollars
upper limit	thousand dollars

5) A poll asked the question, "What do you think is the most important problem facing this country today?" Twenty-five percent of the respondents answered "crime and violence." The margin of sampling error was plus or minus 2 percentage points. Following the convention that the margin of error is based on a 95% confidence interval, find a 95% confidence interval for the percentage of the population that would respond "crime and violence" to the question asked by the pollsters.

lower limit	%
upper limit	%

Answer 1

(1)

(a)

n = 47     

x-bar = 37.5     

s = 7.2     

% = 99     

Standard Error, SE = σ/√n =    7.2 /√47 = 1.050227939

z- score = 2.575829304     

Margin of error = z * SE =     2.57582930354892 * 1.05022793878484 = 2.7052079

Lower Limit of the confidence interval = x-bar - width =      37.5 - 2.70520790012777 = 34.7947921

Upper Limit of the confidence interval = x-bar + width =      37.5 + 2.70520790012777 = 40.2052079

The 99% confidence interval is [34.79, 40.21]

Lower limit = 34.79, Upper limit = 40.21, Margin of error = 2.71

(b)

Confidence Level % = 99

z- score = 2.575829

Population SD, σ = 7.2

Error, E = 2.2

Sample Size, N = (z * σ / E)^2 = (2.575829 * 7.2/2.2)^2 = 72