A random sample of 16 passengers between the two airports flying by ABC Airlines

Question

A random sample of 16 passengers between the two airports flying by ABC Airlines yielded a mean fare of $172. The population standard deviation of the fare is known to be $37.

Part A: Calculate Margin of Error at 97% confidence. Calculate the 97% Confidence Interval on the fare between the two airports for ABC. Interpret the 97% confidence interval calculated. (Please use excel & show formulas used)

Part B: Based on the 97% confidence interval calculated above, “Is the population mean fare between the two airports on ABC Airlines different than $150?" Why or Why not? (Please use excel & show formulas used)

Explanation / Answer

Ans:

As,population standard deviation is known,we use normal(z) distribution.

sample mean=172

population standard deviation=37

n=16

alpha=1-0.97=0.03

alpha/2=0.03/2=0.015

1-alpha/2=1-0.015=0.985

Use excel function normsinv for critical z value:

critical z value=normsinv(0.985)=2.17

a)Margin of error=2.17*(37/sqrt(16))=20.07

97% confidence interval for population mean fare

=172+/-20.07

=(151.93, 192.07)

b)As,above confidenec interval does not include 150 within its limits,so we can conclude that population mean fare between the two airports on ABC Airlines different than $150

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