Question: I had a history of driving to work for the last year, leaving at 5:50 AM averaging 40 minutes with a 10 minute standard deviation. I started going in earlier, leaving at 5:25 AM. I sampled the trips randomly over 32 days and averaged 36 minutes. Does the earlier start have any significance? Test at the 0.05 alpha 1 tail test 

Note: If you perform step 3 correctly you will get a negative value. These are absolute valued tests so Ignore the - sign. These problems depend on the same normal curve. The entire area under the is positive. There are no negative Z values, no critical values that are negative and I am amazed when some of "you" arrive with some skewed reversal of the critical and test statistic the breaks Gauss's laws and mathematical laws.