Question

A national air traffic control system handled an average of 47941 flights during 28 randomly selected days in a recent year. The standard deviation for this sample is 6204 flights per day. Complete parts a through c below.

a. Construct aa 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 to an upper limit of . (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 airlinecompany's claim?

C. 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 contains 50,000, it can be said with 99% confidence that the sample validates the airline company's claim. This is the correct answer.D. Since the 9999% confidence interval does not contain50,000, it cannot be said with 9999% confidence that the sample validates the airline company's claim.

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 not very 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 theStudent's t-distribution. 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

To construct a 99% confidence interval to estimate the average number of flights per day handled by the system, use the formula CI = sample mean ± (critical value) * (standard deviation / sqrt(sample size)). Since the confidence interval does not contain 50000, the sample does not validate the airline company's claim. We need to assume the population follows the normal probability distribution.

Step-by-step explanation:

To construct a 99% confidence interval to estimate the average number of flights per day handled by the system, we can use the formula:

CI = sample mean ± (critical value) * (standard deviation / sqrt(sample size))

Given that the average number of flights is 47941, the standard deviation is 6204, and the sample size is 28, we can calculate:

CI = 47941 ± (2.58) * (6204 / sqrt(28))

Calculating this, we get a confidence interval from approximately 44471 to 51411 flights per day.

Since the confidence interval does not contain 50000, we can conclude that the results from this sample do not validate the airline company's claim.

For this population, we need to assume that the population follows the normal probability distribution.