Add degrees of freedom

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 260 flights from LGB to SFO using Option 1 and records their loading times. The sample mean is found to be 17.5 minutes, with a sample standard deviation of 5.4 minutes. They also select an independent random sample of 225 flights from LGB to SFO using Option 2 and record their loading times. The sample mean is found to be 18.5 minutes, with a sample standard deviation of 4.6 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 0.01 level of significance, is there sufficient evidence to support the claim that the mean Option 1 loading time, H , 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 H and the alternative hypothesis H. P H : I X S p H : 0 (b) Determine the type of test statistic to use. (Choose one) V 0=0 050 020 (c) Find the value of the test statistic. (Round to three or more decimal places.) D*0 00 X (d) Find the p-value. (Round to three or more decimal places.) 5 ? (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