324 CHAPTER 4 COLLECTING DATA 1300 - (b) Explain how you would use the following excerpt from C 1200 the table of random digits to do the random assignment that your design requires. Then use your method to 1100 - make the first three assignments. Sales (9) 1000 - 07511 88915 41267 16853 84569 79367 32337 03316 900 - al 81486 69487 60513 09297 00412 71238 27649 39950 800 - 3.5 4.5 (c) One of the company's officers suggested that it would 3.0 4.0 5.0 5.5 be better to use a matched pairs design instead of Shelf length (ft) a completely randomized design. Explain how you would change your design to accomplish this. (a) Describe the relationship between shelf length and sales. AP1.17 In retail stores, there is a lot of competition for shelf space. There are national brands for most products, b) Write the equation of the least-squares regression lin Be sure to define any variables you use. and many stores carry their own line of in-house brands, too. Because shelf space is not infinite, the (c) If the store manager were to decide to allocate 5 linear question is how many linear feet to allocate to each feet of shelf space to the store's brand of men's product and which shelf (top, bottom, or some- grooming products, what is the best estimate of the where in the middle) to put it on. The middle shelf weekly sales revenue? is the most popular and lucrative, because many (d) Interpret the value of s. shoppers, if undecided, will simply pick the prod- uct that is at eye level. (e) Identify and interpret the coefficient of determination A local store that sells many upscale goods is trying AP1.18 The manager of the store in the preceding exercis to determine how much shelf space to allocate to its calculated the residual for each point in the scatter own brand of men's personal-grooming products. plot and made a dotplot tplot of the residuals. The didthe The middle shelf space is randomly varied between bution of residuals is roughly Normal with a me. 3 and 6 linear feet over the next 12 weeks, and of $0 and standard deviation of $22.92. weekly sales revenue (in dollars) from the store's (a) What percent of the actual sales amounts do you brand of personal-grooming products for men is expect to be within $5 of their expected sales amount recorded. Here is some computer output from the study, along with a scatterplot: (b) The middle 95% of residuals should be between which two values? Use this information to give to give an interval of Predictor Coef SE Coef T P plausible values for the weekly sales rev les revenue if 5 linear Constant 317 . 940 31. 32 10 .15 0 . 000 feet are allocated to the store's brand of men's Shelf length 152 . 680 6 . 445 23 . 69 0 . 000 grooming products. S = 22 . 9212 R-Sq = 98.28 R-Sq (adj ) 98 . 18