The airline industry defines "no-shows" as passengers who have purchased a ticket but fail to arrive at the gate on time for departure. United Airlines operates many flights from Philadelphia to Dallas. The table below represents the observed number of no-shows that occurred on a random sample of 120 flights between Philadelphia and Dallas this year, and experienced the no-show proportions last year. United Airlines would like to know if the proportions of no-shows has changed between last year and this year on flights between these two cities using α = 0.05. The expected frequency of five no-shows for this sample is ________.

Question

The airline industry defines "no-shows" as passengers who have purchased a ticket but fail to arrive at the gate on time for departure. United Airlines operates many flights from Philadelphia to Dallas. The table below represents the observed number of no-shows that occurred on a random sample of 120 flights between Philadelphia and Dallas this year, and experienced the no-show proportions last year.  United Airlines would like to know if the proportions of no-shows has changed between last year and this year on flights between these two cities using α = 0.05. The expected frequency of five no-shows for this sample is ________.

Quizplus · Accepted Answer

To determine the expected frequency of no-shows for this sample, we need to calculate the proportion of no-shows based on last year's data and apply it to the current sample size. Based on the table, the proportion of no-shows last year was 0.08. Therefore, we would expect 0.08 of the 120 flights in the current sample to result in a no-show:

Expected frequency = 0.08 x 120 = 9.6

Since we cannot have a fractional frequency, we round up to 10. Therefore, we would expect 10 flights to result in a no-show in this sample. However, the question specifically asks for the expected frequency of *five* no-shows. To determine this, we need to calculate the probability of having exactly five no-shows in a sample of 120 flights, assuming a no-show rate of 0.08:

P(X = 5) = (120 choose 5) * (0.08)^5 * (0.92)^115 ≈ 0.066

Therefore, the expected frequency of five no-shows in this sample is 0.066 x 120 ≈ 7.92. Since we cannot have a fractional frequency, we round up to 8. However, the question asks for the expected frequency of no-shows, not just five no-shows. Therefore, the best choice is B) 12, which represents the expected frequency of all no-shows in this sample.

The Airline Industry Defines "No-Shows" as Passengers Who Have Purchased