. The Tastee Bakery Company supplies a bakery product to many supermarkets in a metropolitan area. The company wishes to study the effect of the shelf display height employed by the supermarkets on monthly sales (measured in cases of 10 units each) for this product. Shelf display height, the factor to be studied, has three levels - bottom (B), middle (M), and top (T) - which are the treatments. To compare these treatments, the bakery uses a completely randomized experimental design. For each shelf height, fifteen supermarkets (the experimental units) of equal sales potential are randomly selected, and each supermarket displays the product using its assigned height for the month. At the end of the month, sales of the bakery product (the response variable) at the 45 participating stores are recorded. Here we assume that the set of sales amounts for each display height is a sample randomly selected from the population of all sales amounts that could be obtained (at supermarkets of the given sales potential) at that display height. SPSS output is given at the end of the question (beginning on the next page).

1. What is the population mean monthly sales when the product is displayed at the bottom shelf height? At the middle shelf? At the top shelf? Respond with 95% confidence.

1. Based on your results in part (a), is there a statistically significant difference among shelf display heights with respect to mean monthly sales? Defend your answer.

1. A market researcher hypothesized that the population mean monthly sales for the product when displayed at the middle shelf height is greater than 75 cases. Is there clear evidence at the 5% significance level to support the market researcher's hypothesis? Defend your answer.

1. Any concerns about the believability or efficiency of your results in part (c)? Defend your answer

Case Processing Summary shelfheight Cases Valid Missing Total N Percent N Percent N Percent sales Bottom 15 100.0% C 0.0% 15 100.0% Middle 15 100.0% 0 0.0% 15 100.0% Top 15 100.0% 0 0.0% 15 100.0%\fShelfheight = Bottom Descriptives Statistic Std. Error sales Mean 55.387 3708 95% Confidence Interval for Lower Bound Mean Upper Bound 5% Trimmed Mean 55.391 Median 55.500 Variance 2.063 Std. Deviation 1.4362 Minimum 52.5 Maximum 58.2 Range 5.7 Interquartile Range 1.8 Skewness -.104 580 Kurtosis .321 1.121\fOne-Sample Test Test Value = 75 df Sig. (2-tailed) Mean Difference 95% Confidence Interval of the Difference Lower Upper sales -52.891 14 000 -19.6133 -20.409 -18.818Shelfheight = Middle Descriptives Statistic Std. Error sales Mean 77.207 6498 95% Confidence Interval for Lower Bound Mean 75.813 Upper Bound 78.600 5% Trimmed Mean 77. 169 Median 77.500 Variance 6.334 Std. Deviation 2.5166 Minimum 73.0 Maximum 82.1 Range 9.1 Interquartile Range 3.9 Skewness . 198 .580 Kurtosis -.497 1.121 Stem-and-Leaf Plot Frequency Stem & Leaf 3.00 7. 344 10.00 7. 5566788899 2.00 8 . 02T-Test One-Sample Test Test Value = 75 95% Confidence Interval of the t df Sig. (2-tailed) Mean Difference Difference Lower Upper sales 3.396 14 004 2.2067 813 3.600 Shelfheight = Top Descriptives Statistic Std. Error sales Mean 53.327 3537 95% Confidence Interval for Lower Bound Mean 52.568 Upper Bound 54.085 5% Trimmed Mean 53.374 Median 53.200 Variance 1.876 Std. Deviation 1.3698 Minimum 50.9 Maximum 54.9 Range 4.0 Interquartile Range 2.6 Skewness -.441 .580 Kurtosis -1.129 1.121\fOne-Sample Test Test Value = 75 df Sig. (2-tailed) Mean Difference 95% Confidence Interval of the Difference Lower Upper sales -61.279 14 .000 -21.6733 -22.432 -20.915