Final answer:
The question involves conducting a hypothesis test in Statistics to determine if the airline no-show rate is indeed less than 7% using a sample of 382 reservations. The process includes calculating the sample proportion, formulating hypotheses, computing the test statistic, and comparing the p-value to the level of significance.
Step-by-step explanation:
The subject of the question is Statistics, a branch of Mathematics. To address this question, we must conduct a hypothesis test to assess the airline's claim that the no-show rate is less than 7% using a significance level of α = 0.0905. The test statistic can be calculated using the sample proportion πhat (phat) and the hypothesized proportion π (pi). First, we find the sample proportion of no-shows, which is πhat = 23/382.
Next, we formulate the null hypothesis (H0: π ≥ 0.07) and the alternative hypothesis (Ha: π < 0.07). We then calculate the test statistic z = (πhat - π) / √(π(1-π)/n), where π is the hypothesized proportion. Lastly, we determine the p-value using the standard normal distribution and compare it with α to make a decision. If the p-value is less than α, we reject the null hypothesis.