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...

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 230 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 5.2 minutes. They also select an independent random sample of 295 flights from LGB and 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 1and the loading times using Option 2can 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  u1 is less than the mean Option 2 loading time u1 for the airline's flight from LGB to SBO? Perform a one- tailed test.

1. State the null hypothesis Ho and the alternative hypothesis H1?

2. Determine the type of test statistic to use?

3. Find the value of the test statistic?

4. Find the critical value at the 0.05 level of significance?

5. 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?