The mean waiting time at the drive-through of a fast-food restaurant from the time the order is placed to the time it is delivered is 84.3 seconds. A manager devises a new drive-through system that he believes will decrease the wait time. He initiates the new system and measures the wait time for 10 randomly selected orders. The mean wait time for these orders is 78 seconds with a standard deviation of 15.4 seconds. He determines the data is normally distributed. Is his new method effective at the .1 level of significance?
a) state the null hypothesis and the alternative hypothesis
b) sketch the sampling distribution
c) determine the critical values and mark them on your sketch
d) determine the rejection region(s) and shade on your sketch
e) calculate the standardized test statistic and mark on your sketch
f) determine whether to accept or reject the null hypothesis
g) interpret your decision in the context of the original claim. (Be sure to write a complete sentence as your interpretation.)