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 17.6 minutes, with a sample standard deviation of 4.6 minutes. They also select an independent random sample of 280lights 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 3.7 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 0.01level 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.

Carry your intermediate computations to at least three decimal places.

(a)State the null hypothesis

H0

and the alternative hypothesis

H1

.

H0:

H1: Determine the type of test statistic to use.

-Z

-T

-Chi-Square

-F

Find the value of the test statistic. (Round to three or more decimal places.)

Find the p-value. (Round to three or more decimal places.)

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?