2. do pleasant odors work go faster? twenty-one subjects worked a paper-and-pencil maze wearing a mask that was either unscented or carried the smell of flowers. each subject worked the maze three times with each mask, in random order (hint, this is a matched pairs design). here are the differences in their average times (in seconds), unscented minus scented. if the floral small speeds work, the difference will be positive because the time with the scent will be lower. -7.37 -3.14 4.10 -4.40 19.47 -10.80 -.87 8.70 2.94 -17.24 14.30 -24.57 16.17 -7.84 8.60 -10.77 24.97 -4.47 11.90 -6.26 6.67 a. we hope to show that work is faster on the average with the scented mask. state null and alternative hypotheses in terms of the mean difference in times for the population of all adults (2 point). b. find the mean and standard deviations of the 21 observations. did the subjects work faster with the scented mask? is the mean improvement big enough to be important (4 points)? c. test the hypotheses you state in (a) with = .01. is the improvement statistically significant (8 points)?