Question

In: Statistics and Probability

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.

Let μ1 be the population mean for x1 and let μ2 be the population mean for x2. Find an 80% confidence interval for μ1 − μ2. (Round your answers to two decimal places.)

lower limit=

upper limit=

Solutions

Expert Solution

Assume that the distributions of percentage foreign revenue are mound-shaped and symmetric for these two company types.

Due to shape of the distribution we can conclude that these samples come from normal distribution. Since these have different variances we can use t-dist for the confidence interval for independent sample with unequal variances.

X1 X12 X2 X22
1 62.8 3943.84 28 784
2 55.7 3102.49 30.5 930.25
3 47 2209 34.2 1169.64
4 59.6 3552.16 50.3 2530.09
5 55.3 3058.09 11.1 123.21
6 41 1681 28.8 829.44
7 65.1 4238.01 40 1600
8 51.1 2611.21 44.9 2016.01
9 53.4 2851.56 40.7 1656.49
10 50.8 2580.64 60.1 3612.01
11 48.5 2352.25 23.1 533.61
12 44.6 1989.16 21.3 453.69
13 49.4 2440.36 42.8 1831.84
14 61.2 3745.44 18 324
15 39.3 1544.49 36.9 1361.61
16 41.8 1747.24 28 784
17 32.5 1056.25
Total 826.6 43646.94 571.2 21596.14
Mean 51.6625 33.6
SD 7.9277 12.2572

Mean =

SD =

where v1 = n1-1

We only look at the 'df' part.

(1- )% is the confidence interval for population mean

Where = 1- 0.8 = 0.2

df = 28

C.V. =

=

= 1.3125 ............................using t-dist tables

Substituting the value we have

Let μ1 be the population mean for x1 and let μ2 be the population mean for x2. Find an 80% confidence interval for μ1 − μ2. (Round your answers to two decimal places.)

lower limit=

upper limit=

orchestra answered 1 year ago
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