An airline is trying two new boarding procedures, Option 1 and Option 2, to load passengers onto their Long Beach (LGB) to San Francisco (SFO) flights. Since Option 1 has more automation, the airline suspects that the mean Option 1 loading time is less than the mean Option 2 loading time. To see if this is true, the airline selects a random sample of 205 flights from LGB to SFO using Option 1 and records their loading times. The sample mean is found to be 17.7 minutes, with a sample standard deviation of 5.1 minutes. They also select an independent random sample of 270 flights from LGB to SFO using Option 2 and record their loading times. The sample mean is found to be 18.3 minutes, with a sample standard deviation of 4.1 minutes. Since the sample sizes are quite large, it is assumed that the population standard deviation of the loading times using Option 1 and the loading times using Option 2 can be estimated to be the sample standard deviation values given above. At the 0.05 level of significance, is there sufficient evidence to support the claim that the mean Option 1 loading time, μ1, is less than the mean Option 2 loading time, μ2, for the airline's flights from LGB to SFO? Perform a one-tailed test. Then complete the parts below.
