Question

A national air traffic control system handled an average of

47 comma 474

flights during

28

randomly selected days in a recent year. The standard deviation for this sample is

6 comma 376

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 does not contain​ 50,000, it cannot be said with

99

​%

confidence that the sample validates the airline​ company's claim.

B.

Since the

99

​%

confidence interval contains​ 50,000, it cannot be said with

99

​%

confidence that the sample validates the airline​ company's 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​ company's claim.

D.

Since the

99

​%

confidence interval contains​ 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 follows the​ Student's t-distribution.

B.

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.

C.

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.

D.

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

Answer 1

Solution:

Given:

n = 28

s = 6,376

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 = 28 - 1 = 27

Look in  t table for df = 27 and two tail area = 0.01 and find t critical value

t_c = 2.771

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 44,135 to an upper limit of 50,813.

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

D. 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) What assumptions need to be made about this​ population?

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