1. During September 2018, United Airlines introduced a new two-line boarding process intended to decrease gate congestion, passenger anxiety, and time to board the plane. Independent random samples of similar cross-country flights for United Airlines and American Airlines were obtained and the boarding time (in minutes) for each was recorded. Assume both populations are normally distributed and the population standard deviations are unequal.

Given, n1=12n2=15x1=42.5x2=49.9s1=11.1s2=15.1α=0.05 The degrees of freedom is obtained as- df=s12n1+s22n22s12n12n1-1+s22n22n2-1=11.1212+15.1215211.1212212-1+15.1215215-1=24.86 The hypothesis to be tested here is- H0:μ1=μ2H1:μ1<μ2 This is a left tailed test. The test statistics is obtained as- t=x1-x2s12n1+s22n2=42.5-49.911.1212+15.1215=-1.466The p-value for the test statistics is obtained by using excel syntax- Decision rule: Reject H0: if p-value<0.05 Conclusion: Since p-value(0.077814)>0.05, therefore there is no evidence to reject the null hypothesis and can be concluded that there is no evidence to suggest that the new United Airlines boarding process takes less time than the American Airlines boarding process. Committing type I error here implies rejecting the null hypothesis that there is no difference between new United Airlines boarding process and the American Airlines boarding process when actually there is no difference. Committing type II error here implies accepting the null hypothesis that there is no difference between new United Airlines boarding process and the American Airlines boarding process when actually new United Airlines boarding process takes less time than the American Airlines boarding process.