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.t Technology companies, % foreign revenue: x₁; n₁ = 16 47.0 48.5 59.6 44.6 55.3 49.4 41.0 61.2 65.1 39.3 Another independent random sample of basic consumer product companies (Goodyear, Sarah Lee, H.J. Heinz, Toys 'R' Us) gave the following information. 62.8 53.4 55.7 50.8 = LAUSE SALT Basic consumer product companies, % foreign revenue: x₂; ₂ = 17 44.9 28.0 30.5 40.7 60.1 34.2 23.1 11.1 42.8 28.0 32.5 50.3 21.3 % 28.8 40.0 18.0 36.9 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 four decimal places.) x₁ x1 % S₁ = % x₂ = % $₂ = 51.1 41.8 (b) Let u be the population mean for x, and let ₂ be the population mean for x₂. Find a 95% confidence interval for H₁ - H₂. (Round your answers to two decimal places.) lower limit % upper limit % (c) Examine the confidence interval and explain what it means in the context of this problem. Does the interval consist of numbers that are all positive? all negative? of different signs? At the 95% level of confidence, do technology companies have a greater percentage foreign revenue than basic consumer product companies? O We can not make any conclusions using this confidence interval. O Because the interval contains only negative numbers, we can say that technology companies receive a lower percent of foreign revenue. O Because the interval contains only positive numbers, we can say that technology companies receive a higher percent of foreign revenue. O Because the interval contains both positive and negative numbers, we can not say that technology companies receive a higher percent of foreign revenue. (d) Which distribution (standard normal or Student's t) did you use? Why? O Student's t was used because ₁ and ₂ are known. O Standard normal was used because o, and a₂ are unknown. O Student's t was used because ₁ and ₂ are unknown. O Standard normal was used because a, and a2 are known.
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.t Technology companies, % foreign revenue: x₁; n₁ = 16 47.0 48.5 59.6 44.6 55.3 49.4 41.0 61.2 65.1 39.3 Another independent random sample of basic consumer product companies (Goodyear, Sarah Lee, H.J. Heinz, Toys 'R' Us) gave the following information. 62.8 53.4 55.7 50.8 = LAUSE SALT Basic consumer product companies, % foreign revenue: x₂; ₂ = 17 44.9 28.0 30.5 40.7 60.1 34.2 23.1 11.1 42.8 28.0 32.5 50.3 21.3 % 28.8 40.0 18.0 36.9 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 four decimal places.) x₁ x1 % S₁ = % x₂ = % $₂ = 51.1 41.8 (b) Let u be the population mean for x, and let ₂ be the population mean for x₂. Find a 95% confidence interval for H₁ - H₂. (Round your answers to two decimal places.) lower limit % upper limit % (c) Examine the confidence interval and explain what it means in the context of this problem. Does the interval consist of numbers that are all positive? all negative? of different signs? At the 95% level of confidence, do technology companies have a greater percentage foreign revenue than basic consumer product companies? O We can not make any conclusions using this confidence interval. O Because the interval contains only negative numbers, we can say that technology companies receive a lower percent of foreign revenue. O Because the interval contains only positive numbers, we can say that technology companies receive a higher percent of foreign revenue. O Because the interval contains both positive and negative numbers, we can not say that technology companies receive a higher percent of foreign revenue. (d) Which distribution (standard normal or Student's t) did you use? Why? O Student's t was used because ₁ and ₂ are known. O Standard normal was used because o, and a₂ are unknown. O Student's t was used because ₁ and ₂ are unknown. O Standard normal was used because a, and a2 are known.
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Author:Amos Gilat
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Transcribed Image Text: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.t
Technology companies, % foreign revenue: X₁; ₁ 16
41.0 65.1
61.2 39.3
47.0
62.8 55.7
53.4 50.8 48.5
Another independent random sample of basic consumer product companies (Goodyear, Sarah Lee, H.J. Heinz, Toys 'R' Us) gave the following information.
59.6
44.6
55.3
49.4
Basic consumer product companies, % foreign revenue: x2; n₂ = 17
28.0 30.5 34.2 50.3 11.1
40.7 60.1 23.1 21.3 42.8
32.5
40.0 44.9
36.9 28.0
USE SALT
28.8
18.0
51.1
41.8
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 four decimal places.)
%
X₁ =
%
S₁ =
%
X2 =
$2 =
%
(b) Let u₁ be the population mean for x₁ and let ₂ be the population mean for X₂. Find a 95% confidence interval for H₁ - H₂. (Round your answers to two decimal places.)
lower limit
%
upper limit
%
(d) Which distribution (standard normal or Student's t) did you use? Why?
O Student's t was used because ₁ and ₂ are known.
O Standard normal was used because a₁ and a2 are unknown.
(c) Examine the confidence interval and explain what it means in the context of this problem. Does the interval consist of numbers that are all positive? all negative? of different signs? At the 95 % level of confidence, do technology companies have a
greater percentage foreign revenue than basic consumer product companies?
O We can not make any conclusions using this confidence interval.
O Because the interval contains only negative numbers, we can say that technology companies receive a lower percent of foreign revenue.
O Because the interval contains only positive numbers, we can say that technology companies receive a higher percent of foreign revenue.
O Because the interval contains both positive and negative numbers, we can not say that technology companies receive a higher percent of foreign revenue.
O Student's t was used because o, and a2 are unknown.
1
O Standard normal was used because a₁ and ₂ are known..
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VIEWStep 2: Computing the sample mean standard deviations for X1 and X2
VIEWStep 3: Computing a 95% confidence interval for ? 1 − ? 2
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VIEWStep 5: Stating the reason for the distribution used the compute the confidence interval
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