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For large U.S. companies, what percentage of their total income comes from foreign sales? A random...

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 μ1 be the population mean for x1 and let μ2 be the population mean for x2. Find a 98% confidence interval for μ1 − μ2. (Round your answers to two decimal places.)

lower limit      %
upper limit      %

Solutions

Expert Solution

Technology companie ( X ) Σ ( Xi- X̅ )2 consumer product ( Y ) Σ ( Yi- Y̅ )2
62.8 124.0996 28 31.36
55.7 16.3216 30.5 9.61
47 21.7156 34.2 0.36
59.6 63.0436 50.3 278.89
55.3 13.2496 11.1 506.25
41 113.6356 28.8 23.04
65.1 180.6336 40 40.96
51.1 0.3136 44.9 127.69
53.4 3.0276 40.7 50.41
50.8 0.7396 60.1 702.25
48.5 9.9856 23.1 110.25
44.6 49.8436 21.3 151.29
49.4 5.1076 42.8 84.64
61.2 91.0116 18 243.36
39.3 152.7696 36.9 10.89
41.8 97.2196 28 31.36
32.5 1.21
Total 826.6 942.7176 571.2 2403.82

Mean X̅ = Σ Xi / n
X̅ = 826.6 / 16 = 51.66
Sample Standard deviation SX = √ ( (Xi - X̅ )2 / n - 1 )
SX = √ ( 942.7176 / 16 -1 ) = 7.93

Mean Y̅ = ΣYi / n
Y̅ = 571.2 / 17 = 33.6
Sample Standard deviation SY = √ ( (Yi - Y̅ )2 / n - 1 )
SY = √ ( 2403.82 / 17 -1) = 12.26

Part a)

X1 = 51.66

S1 = 7.93

X2 = 33.60

S2 = 12.26

Part b)

Confidence interval :-

t(α/2, DF) = t(0.02 /2, 27 ) = 2.473



DF = 27


Lower Limit =
Lower Limit = 9.23
Upper Limit =
Upper Limit = 26.90
98% Confidence interval is ( 9.23 , 26.90 )


milcah answered 10 months ago
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