Question

a national air traffic control system handled an average of 47,708 flights during 29 randomly selected days in a recent year. the standard deviation for this sample is 6,486 flights per day. complete parts a through c below.
a. construct a 99% confidence interval to estimate the average number of flights per day handled by the system.
the 99% confidence interval to estimate the average number of flights per day handled by the system is from a lower limit of 44,379 to an upper limit of 51,037.
(round to the nearest whole numbers.)
b. suppose an airline company claimed that the national air traffic control system handles an average of 50,000 flights per day. do the results from this sample validate the airline companys claim?
a. since the 99% confidence interval contains 50,000, it can be said with 99% confidence that the sample validates the airline companys claim.
b. since the 99% confidence interval contains 50,000, it cannot be said with 99% confidence that the sample validates the airline companys claim.
c. since the 99% confidence interval does not contain 50,000, it can be said with 99% confidence that the sample validates the airline companys claim.
d. since the 99% confidence interval does not contain 50,000, it cannot be said with 99% confidence that the sample validates the airline companys claim.

Explanation:

Step1: Recall confidence - interval concept

A confidence interval gives a range of values within which the population parameter is likely to lie. If a claimed value lies within the confidence interval, we cannot reject the claim at the given confidence level.

Step2: Analyze the given confidence interval and claim

The 99% confidence interval for the average number of flights per day is from 44,379 to 51,037. The airline company's claim is that the average number of flights per day is 50,000. Since 50,000 lies within the interval (44,379, 51,037), it can be said with 99% confidence that the sample validates the airline company's claim.

Answer:

A. Since the 99% confidence interval contains 50,000, it can be said with 99% confidence that the sample validates the airline company's claim.