In: Statistics and Probability
The mean number of flying times for pilots at Southwest Airlines is X ̅ = 80 hours per month. Assume that this mean was based on actual flying times for a sample of n = 25 Southwest Airlines pilots and that the sample standard deviation was S = 8.5 hours.
a.Construct and interpret a 95% confidence interval estimate of the population mean flying time for the Southwest Airlines pilots.
b.What is the margin of error in part a?
Solution :
Given that,
= 80
s = 8.5
n = 25
Degrees of freedom = df = n - 1 = 25 - 1 = 24
a ) At 95% confidence level the t is ,
= 1 - 95% = 1 - 0.95 = 0.05
/ 2 = 0.05 / 2 = 0.025
t /2,df = t0.025,24 =2.797
b ) Margin of error = E = t/2,df * (s /n)
= 2.797 * (8.5/ 25)
= 4.75
Margin of error = 4.75
The 99% confidence interval estimate of the population mean is,
- E < < + E
80 - 4.75 < < 80 + 4.75
75.25 < < 84.75
(75.25, 84.75 )