Homework SourseFor large US companies what percentage of their total income
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.†
Another independent random sample of basic consumer product companies (Goodyear, Sarah Lee, H.J. Heinz, Toys \'R\' Us) gave the following information.
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.)
(b) Let 1 be the population mean for x1 and let 2 be the population mean for x2. Find a 99% confidence interval for 1 2. (Round your answers to two decimal places.)
| 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 |
Solution
a)
Mean(x1)=51.663
Standard deviation( sd1 )=7.928
Sample Size(n1)=16
Mean(x2)=33.6
Standard deviation( sd2 )=12.257
Sample Size(n1)=17
b)
CI = x1 - x2 ± t a/2 * Sqrt ( sd1 ^2 / n1 + sd2 ^2 /n2 )
Where,
x1 = Mean of Sample 1, x2 = Mean of sample2
sd1 = SD of Sample 1, sd2 = SD of sample2
a = 1 - (Confidence Level/100)
ta/2 = t-table value
CI = Confidence Interval
CI = [ ( 51.663-33.6) ±t a/2 * Sqrt( 62.853184/16+150.234049/17)]
= [ (18.06) ± t a/2 * Sqrt( 12.77) ]
= [ (18.06) ± 2.947 * Sqrt( 12.77) ]
= [7.53 , 28.59]
