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 ______.
A) 9
B) 12
C) 14
D) 19

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 ______.
A) 9 
B) 12 
C) 14 
D) 19

Quizplus · Accepted Answer

To determine the expected frequency of no-shows, we first need to calculate the proportion of no-shows for last year: 180/300 = 0.6. Then, we can use this proportion to calculate the expected frequency for this year: 0.6 * 120 = 72. However, we need to adjust for the fact that the expected frequency is less than 5, which violates the assumptions of the chi-square test. To do this, we can combine adjacent categories until each expected frequency is at least 5. For example, we can combine the categories of 0 and 1 no-shows, which have an observed frequency of 37 and an expected frequency of 36. We can also combine the categories of 4 and 5 no-shows, which have an observed frequency of 3 and an expected frequency of 7. This leaves us with 6 categories: 0-1, 2, 3, 4-5, 6-7, and 8 or more. We can calculate the expected frequencies for these categories using the adjusted proportion of no-shows (0.6/6 = 0.1): 36, 22, 32, 7, 13, and 10. Adding up these expected frequencies gives us 120, which is the total number of flights in the sample. The expected frequency of five no-shows is therefore 7.

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