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 the sample is 6,486 flights per day. complete parts a through c below. 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. 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 students t - distribution. b. since the sample size is not greater than or equal to 30, one needs to assume that the population follows the students 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. 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.

Explanation:

Step1: Recall confidence - interval concept

If the claimed value lies within the confidence interval, we cannot reject the claim at the corresponding confidence level. If it lies outside, we can reject the claim. Also, for small - sample (n < 30) confidence intervals when the population standard deviation is unknown, we assume the population is normally distributed.

Step2: Analyze part a

For the claim validation, if 50,000 is in the 99% confidence interval, we cannot say with 99% confidence that the sample does not validate the claim. If 50,000 is not in the 99% confidence interval, we cannot say with 99% confidence that the sample validates the claim.

Step3: Analyze part b

When the sample size n = 29 (<30) and the population standard deviation is unknown (we are given the sample standard deviation), we use the t - distribution. The key assumption is that the population follows the normal probability distribution.

Answer:

a. D. 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. 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.