Testing No-Show Rate Claim of an Airline

Is the no-show rate for passengers really less than 5%?

In a sample of 420 randomly selected reservations, 19 were no-shows. Should the airline's claim of less than 5% be tested?

Answer:

Yes, we need to test the airline's claim regarding the no-show rate.

In order to test the claim made by the airline about the no-show rate being less than 5%, we need to conduct a hypothesis test. The sample data provides crucial information that allows us to assess whether the claim is statistically significant or not.

Given that the sample size (n) is 420 and the number of no-shows (x) is 19, the sample proportion can be calculated as follows:

Sample proportion (p') = x/n = 19/420 ≈ 0.045

The hypothesis test involves setting up the null hypothesis (H₀) and the alternative hypothesis (H₁) as follows:

H₀: p = 0.05

H₁: p < 0.05

The test statistic (z) can be computed using the sample proportion and the given proportion of no-shows:

z = (p' - p) / √(p(1-p)/n)

z = (0.045 - 0.05) / √(0.05(1-0.05)/420) ≈ -0.164

Based on the test statistics, we can evaluate the significance of the claim and determine whether the observed sample percentage supports the airline's assertion regarding the no-show rate.