1-16
a. Sample proportion of Arizonian deaths that are due to respiratory disease: P = 1440/18000 = 0.08
Sample size: n=18000
Confidence interval (95%): P +/- (1.96 * sqrt((P)(1-P)/n))
(0.076, 0.084)

b. Sample proportion of United States deaths that are due to respiratory disease: P = 110000/1900000 = 0.058 (approx)
Sample size: n=1900000
Confidence interval (95%): P +/- (1.96 * sqrt((P)(1-P)/n))
(0.0576, 0.0582)

c. It seems that Arizona may have a higher proportion of deaths from respiratory disease than the US as a whole (if we assume that these sample proportions are based on a random sample). However, we shouldn't jump to the conclusion that Arizona's climate worsens respiratory disease. One alternate explanation (there are others): People who already have respiratory disease may be moving to Arizona, in an effort to alleviate their symptoms. As a result, there may be a higher proportion of the Arizonian population with respiratory disease. Then, it is likely that a farily high proportion of deaths will be due to respiratory disease, just because such a high proportion of people have this condition.

1-18

a. Overall proportion of men admitted: 3700/8300 = 0.45 (approx)
Overall proportion of women admitted: 1500/4300 = 0.35 (approx)
The percentage of men accepted is 10% higher than the percentage of women.

b. Proportion of men admitted for science: 3000/6000 = 0.50
Proportion of men admitted for the arts: 700/2300 = 0.30 (approx)

Proportion of women admitted for science: 600/1100 = 0.55(approx)
Proportion of women admitted for the arts: 900/3200 = 0.28 (approx)

The percentage of men accepted for the arts is 2% higher than the percentage of women. The percentage of men accepted for science is 5% lower than the percentage of women.

c. More women are applying to the arts, which has a lower overall acceptance rate (29%) than the sciences (51%).

d.
i. tougher, lower
ii. accurate
iii.regression analysis

2-6

a.Draw a frequency histogram.
b.median:11 million, first quartile: 6 million, third quartile: 39 million
c.Draw a box plot.

2-14

a.
i. 107
ii. 102
iii. 105
iv. 105

b. True, the formula is correct.

2-18

a.Q1 = 10, Q3 = 20, IQR = 10
b.s = 5.401 (approx)

2-24

a.sample mean = 6.08oz, s = 0.081oz (approx), CV = 0.013 (approx)
b.sample mean = 0.38lbs, s = 0.005lbs (approx), CV = 0.013 (approx)
c.cost in dollars = 0.24 + (0.42*weight in ounces) sample mean = $2.79, s = $0.03 (approx), CV = 0.01 (approx)

2-30

a.Just look at the graph and approximate as best you can. I'd say that it looks like the U.S. population is about 1.75 times larger than the Brazilian population.

b.The shape of the graphs for the 2 nations is very different. The U.S. graph has a substantial bulge in the middle (large population of people close to 30), while the graph for Brazil is almost pyramidal. (As the age categories get higher, there are fewer people in them.)

c.The pyramids taper off at the top due to the fact that only a relatively small portion of the population reach very old ages. To speak very harshly, the graph starkly depicts the elderly portion of the population gradually "dying off".

d."baby boom" peaked about 1955 or so, producing a large number of people ("baby boomers") aged 25-30 in 1985.
first "baby bust" peaked about 1930-1935, and a much larger one about 1975-1980.

e.Over the next two decades, the average age of Americans will very likely increase.
In the next 30-40 years, there will likely be a large increase in the social security burden to fund retirement, as the relative number of people under 65 paying for it shows a large decrease.

2-34

a.Since the mean ($27,000) is higher than the median ($22,000), the distribution is skewed to the right.
b.The total income for the whole country is (87,000,000)($27,000) = $2,349,000,000,000

2-36

a.The average forecast was about 5.4%, which was higher than what actually occurred.
b.The sample standard deviation for this group of predictions is about 1.4%.

2-42

a.Using the manager's estimated frequencies for the hybrids:
mean profit = $272
SD of profit = $115 (approx)

b.Total profits:
Current breed of cattle: ($294)(600) =$176,400
Proposed breed of cattle: ($272)(750) = $204,000
Given the data for the current breed and the estimates for the proposed breed, the total profit that he makes with the proposed breed looks higher than what he made with the current breed. Even though the average profit per head is smaller, a higher percentage of proposed breed actually bring a profit; also, he will be able to raise more of them.

c.If the mean profit per head of the proposed breed of cattle were $235.20 ($176,400/750), then the total profit made for either breed would be the same ($176,400). If the mean profit per head of the proposed breed of cattle were less than $235.20, then the manager would be better off with the current breed.