Defining the null and alternative hypotheses, we make use of the on-time rates for two airlines. We conduct a hypothesis test using a two-proportion z-test. Based on the p-value outcome, we determine if there's significant statistical evidence to prove Airline 2 is more reliable than Airline 1.
In hypothesis testing, we're trying to find if there's a significant difference between two proportions, in this case, the on-time rates of two airlines. We have Airline 1 with 126 out of 155 flights on time and Airline 2 with 136 out of 155 flights on time. First, we calculate the observed proportions: p1 (Airline 1) = 126/155 = 0.8129 and p2 (Airline 2) = 136/155 = 0.8774.
Let's define our null hypothesis (H0) and our alternative hypothesis (Ha). H0: p1 = p2 (There's no difference.) and Ha: p1 < p2 (Airline 1 has a lower on-time rate compared to Airline 2, suggesting that Airline 2 is more reliable.). We perform a two-proportion z-test using a significance level of 0.01. If the p-value is less than 0.01, we reject H0 and conclude there's enough evidence to say Airline 2 is more reliable than Airline 1. If it's larger, we do not reject H0, and there's not enough statistical evidence to determine which airline is more reliable.