Pleasant smells. Do pleasant odors help 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. (This is a matched pairs design.) Here are the differences in their average times (in seconds), unscented minus scented.

If the floral smell 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 −0.87 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

μ for the population of all adults.

Part IV Review Exercises 553

(b) Using a calculator, find the mean and standard deviation of the 21 observations. Did the subjects work faster with the scented mask? Is the mean improvement big enough to be important?

(c) Make a stemplot of the data (round to the nearest whole second). Are there outliers or other problems that might hinder inference?

(d) Test the hypotheses you stated in (a). Is the improvement statistically significant?