Question

An airline claims that the no-show rate for passengers is less than 5%. In a sample of 420 randomly selected reservations, 19 were no-shows. At α=0.01, test the airline's claim. State the sample percentage and round it to three decimal places.

State the hypotheses.
State the critical value(s).
State the test statistics.
State the decision
State the conclusion.

Answer 1

To test the airline's claim, we conduct a hypothesis test. The null hypothesis is that the no-show rate is equal to or greater than 5%, and the alternative hypothesis is that the no-show rate is less than 5%.

Step-by-step explanation:

To test the airline's claim, we need to conduct a hypothesis test. The null hypothesis (H0) is that the no-show rate is equal to or greater than 5% (p ≥ 0.05). The alternative hypothesis (Ha) is that the no-show rate is less than 5% (p < 0.05).

Using the given data, the sample percentage of no-shows is 19/420 = 0.0452 (rounded to three decimal places). We need to calculate the test statistic and compare it to the critical value to make a decision.

To calculate the test statistic, we can use the formula: z = (p - P) / sqrt((P * (1 - P)) / n), where P is the hypothesized no-show rate (0.05), p is the sample percentage, and n is the sample size.

Plugging in the values, we find the test statistic to be approximately -2.574. The critical value for a one-tailed test with α = 0.01 is -2.326.

Since the test statistic (-2.574) is less than the critical value (-2.326), we reject the null hypothesis.

Therefore, we have sufficient evidence to conclude that the no-show rate for passengers is indeed less than 5% based on the sample data.