Using techniques from an earlier section, we can find a confidence interval for μ_{d}. Consider a random sample of n matched data pairs A, B. Let d = B − A be a random variable representing the difference between the values in a matched data pair. Compute the sample mean
d
of the differences and the sample standard deviation s_{d}. If d has a normal distribution or is moundshaped, or if n ≥ 30, then a confidence interval for μ_{d} is as follows.
d − E < μ_{d} < d + E
where E =
t_{c}
s_{d}  

c = confidence level (0 < c < 1)
t_{c} = critical value for confidence level
c and d.f. = n − 1
B: Percent increase for company 
16  6  14  18  6  4  21  37 
A: Percent
increase for CEO 
25  14  23  14 
−4 
19  15  30 
(a) Using the data above, find a 95% confidence interval for the mean difference between percentage increase in company revenue and percentage increase in CEO salary. (Round your answers to two decimal places.)
lower limit  
upper limit 
a)
for 95% CI; and 7 degree of freedom, value of t=  2.365  
therefore confidence interval=sample mean /+ t*std error  
margin of errror =t*std error=  7.917  
lower confidence limit =  9.67  
upper confidence limit =  6.17 
Get Answers For Free
Most questions answered within 1 hours.