Question

A.) Inorganic phosphorous is a naturally occurring element in all plants and animals, with concentrations increasing progressively up the food chain (fruit < vegetables < cereals < nuts < corpse). Geochemical surveys take soil samples to determine phosphorous content (in ppm, parts per million). A high phosphorous content may or may not indicate an ancient burial site, food storage site, or even a garbage dump. The Hill of Tara is a very important archaeological site in Ireland. It is by legend the seat of Ireland's ancient high kings†. Independent random samples from two regions in Tara gave the following phosphorous measurements (ppm). Assume the population distributions of phosphorous are mound-shaped and symmetric for these two regions.

Region I: x1; n1 = 12
540	810	790	790	340	800
890	860	820	640	970	720

Region II: x2; n2 = 16
750	870	700	810	965	350	895	850
635	955	710	890	520	650	280	993

(a) Use a calculator with mean and standard deviation keys to calculate x₁, s₁, x₂, and s₂. (Round your answers to one decimal place.)

x1	= ppm
s1	= ppm
x2	= ppm
s2	= ppm

(b) Let ?₁ be the population mean for x₁ and let ?₂ be the population mean for x₂. Find a 90% confidence interval for

?₁ ? ?₂. (Round your answers to one decimal place.)

lower limit	ppm
upper limit	ppm

B.) For large U.S. companies, what percentage of their total income comes from foreign sales? A random sample of technology companies (IBM, Hewlett-Packard, Intel, and others) gave the following information.†

Technology companies, % foreign revenue: x1; n1 = 16
62.8	55.7	47.0	59.6	55.3	41.0	65.1	51.1
53.4	50.8	48.5	44.6	49.4	61.2	39.3	41.8

Another independent random sample of basic consumer product companies (Goodyear, Sarah Lee, H.J. Heinz, Toys 'R' Us) gave the following information.

Basic consumer product companies,% foreign revenue: x2; n2 = 17
28.0	30.5	34.2	50.3	11.1	28.8	40.0	44.9
40.7	60.1	23.1	21.3	42.8	18.0	36.9	28.0
32.5

Assume that the distributions of percentage foreign revenue are mound-shaped and symmetric for these two company types. (a) Use a calculator with mean and standard deviation keys to calculate x₁, s₁, x₂, and s₂. (Round your answers to two decimal places.)

x1 =	%
s1 =	%
x2 =	%
s2 =	%

(b) Let ?₁ be the population mean for x₁ and let ?₂ be the population mean for x₂. Find a 90% confidence interval for

?₁ ? ?₂. (Round your answers to two decimal places.)

lower limit		%
upper limit		%

C.) Independent random samples of professional football and basketball players gave the following information.

Heights (in ft) of pro football players: x₁; n₁ = 45

6.32	6.51	6.50	6.25	6.50	6.33	6.25	6.17	6.42	6.33
6.42	6.58	6.08	6.58	6.50	6.42	6.25	6.67	5.91	6.00
5.83	6.00	5.83	5.08	6.75	5.83	6.17	5.75	6.00	5.75
6.50	5.83	5.91	5.67	6.00	6.08	6.17	6.58	6.50	6.25
6.33	5.25	6.66	6.50	5.81

Heights (in ft) of pro basketball players: x₂; n₂ = 40

6.05	6.56	6.25	6.58	6.25	5.92	7.00	6.41	6.75	6.25
6.00	6.92	6.81	6.58	6.41	6.67	6.67	5.75	6.25	6.25
6.50	6.00	6.92	6.25	6.42	6.58	6.58	6.08	6.75	6.50
6.83	6.08	6.92	6.00	6.33	6.50	6.58	6.82	6.50	6.58

(a) Use a calculator with mean and standard deviation keys to calculate x₁, s₁, x₂, and s₂. (Round your answers to three decimal places.)

x1 =
s1 =
x2 =
s2 =

(b) Let ?₁ be the population mean for x₁ and let ?₂ be the population mean for x₂. Find a 90% confidence interval for ?₁ – ?₂. (Round your answers to three decimal places.)

lower limit
upper limit

Answer 1

A)

(a)

x1	=747.5 ppm
s1	=170.4 ppm
x2	=738.9 ppm
s2	=212.1 ppm

(b)

90% confidence interval for ?1 ? ?2 (assume equal variances)

lower limit   -118.8	ppm
upper limit  136.0	ppm

B.a.

x1 =	51.66%
s1 =	7.93%
x2 =	33.60%
s2 =	12.26%

(b)

90% confidence interval for ?1 ? ?2. (assume equal variances)

lower limit		11.93%
upper limit		24.20%

C.

a.

x1 = 6.180
s1 =0.3691
x2 =6.4512
s2 =0.3141

(b) 90% confidence interval for ?1 – ?2 (aasuming equal variances) is

lower limit =-0.395
upper limit = -0.146 where, s= Pooled StDev = 0.3444,