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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 250 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 7 minutes They also select an independent random sample of 240 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 5 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 u is less than the mean Option 2 loading time 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 Ho and the alternative hypothesis H Ho H 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 critical value at the 0 05 level of significance Round to three or more decimal places 0 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 OYes No x X 4 0 0 X O S 2 OSO 0 0 P olo 020 O

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