For large U.S. companies, what percentage of their total income comes from forei
ID: 3218838 • Letter: F
Question
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. (Reference: Forbes Top Companies.) 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 x_1, s_1, x_2, and s_2. (Use 2 decimal places.) (b) Let mu_1 be the population mean for x_1 and let mu_2 be the population mean for x_2. Find an 80% confidence interval for mu_1 - mu_2. (Use 2 decimal places.) lower limit upper limitExplanation / Answer
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
Mean(x1)=51.66
Standard deviation( sd1 )=7.93
Sample Size(n1)=16
Mean(x2)=33.6
Standard deviation( sd2 )=12.26
Sample Size(n2)=17
CI = [ ( 51.66-33.6) ±t a/2 * Sqrt( 62.8849/16+150.3076/17)]
= [ (18.06) ± t a/2 * Sqrt( 12.7719) ]
= [ (18.06) ± 1.341 * Sqrt( 12.7719) ]
= [13.2676 , 22.8524] ~ [ 13.27, 22.85 ]
Interpretations:
1) We are 80% sure that the interval [13.2676 , 22.8524] contains the difference between
true population mean U1 - U2
2) If a large number of samples are collected, and a confidence interval is created
for each sample, 80% of these intervals will contains the difference between
true population mean U1 - U2
3) Since this Cl does n't contain a zero we can't conclude at 0.01 true mean
difference is zero
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.