Question

A national air traffic control system handled an average of 47 comma 779 flights during 29 randomly selected days in a recent year. The standard deviation for this sample is 6 comma 218 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 nothing to an upper limit of nothing . ​(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​ company's claim? A. Since the 99 ​% confidence interval contains​ 50,000, it cannot be said with 99 ​% confidence that the sample validates the airline​ company's claim. B. Since the 99 ​% confidence interval does not contain​ 50,000, it cannot be said with 99 ​% confidence that the sample validates the airline​ company's claim. C. Since the 99 ​% confidence interval contains​ 50,000, it can be said with 99 ​% confidence that the sample validates the airline​ company's claim. D. Since the 99 ​% confidence interval does not contain​ 50,000, it can be said with 99 ​% confidence that the sample validates the airline​ company's claim. c. What assumptions need to be made about this​ population? A. Since the sample size is not greater than or equal to​ 30, one needs to assume that the population distribution is skewed to one side. B. Since the sample size is not greater than or equal to​ 30, one needs to assume that the population follows the normal probability distribution. C. Since the sample size is not greater than or equal to​ 30, one needs to assume that the population distribution is not very skewed to one side. D. Since the sample size is not greater than or equal to​ 30, one needs to assume that the population follows the​ Student's t-distribution.

Answer 1

Solution:

Given:

n = 29

s = 6,218

Part a. Construct a 99 ​% confidence interval to estimate the average number of flights per day handled by the system.

Formula:

where

t_c is t critical value for c = 99%  confidence level

Thus two tail area = 1 - c = 1 - 0.99 = 0.01

df = n - 1 = 29 - 1 = 28

Look in  t table for df = 28 and two tail area = 0.01 and find t critical value

t_c = 2.763

thus

Thus

The 99 ​% confidence interval to estimate the average number of flights per day handled by the system is from a lower limit of 44,589 to an upper limit of 50,969.

Part b)

Claim:  the national air traffic control system handles an average of​ 50,000 flights per day.

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

Part c)

B. Since the sample size is not greater than or equal to​ 30, one needs to assume that the population follows the normal probability distribution.