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} = t_{0.025,24} =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 )

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?

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