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. 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 tru airline selects a random sample of 245 flights from LGB to SFO using Option 1 and records their loading times. The sample mean is found to be 17.7 min with a sample standard deviation of 5.6 minutes. They also select an independent random sample of 295 flights from LGB to SFO using Option 2 and reco their loading times. The sample mean is found to be 18.3 minutes, with a sample standard deviation of 4.0 minutes. Since the sample sizes are quite large 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 samp 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 tim , 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. Carry your intermediate computations to at least three decimal places. (If necessary, consult a list of formulas.) (a) State the null hypothesis H, and the alternative hypothesis H₁. H O Р Ho :D H₁:0 (b) Determine the type of test statistic to use. (Choose one) (c) Find the value of the test statistic. (Round to three or more decimal places.) (d) Find the p-value. (Round to three or more decimal places.) (e) Can we support the claim that the mean Option 1 loading time is less than the mean Option 2 loading time for the airline's flights from LGB to SFO? Yes No Ix X 9 X P S 00 OSO 020 O0 3 ? plo

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