In a preliminary study to examine the effectiveness of three different commercials for an upcoming promotion (labeled C1, C2, and C3), 40 consumers were selected to view each commercial and rate it on a 5-point Likert scale, with 1 being the worst and 5 being the best. The results of this study are given below. Use Excel to test whether there is evidence to conclude that there is a difference between the effectiveness of the 3 commercials and interpret the results (in the spaces indicated below). Rating Results Commercial C1 C2 C3 4 3 2 4 4 4 3 3 4 2 3 2 2 3 3 1 4 2 3 5 2 3 3 3 4 3 5 3 4 2 4 3 4 2 3 3 4 2 2 3 4 4 3 4 3 3 3 3 Place Excel Generated Output Below (starting in cell F4) State the Null and Alternative Hypothesis. 4 5 2 H0: 3 3 3 4 2 3 2 2 4 4 3 3 4 3 2 4 3 3 3 5 4 3 4 5 3 4 3 2 5 2 4 1 4 5 2 3 3 4 3 2 3 4 3 4 1 2 4 2 4 3 2 4 3 2 3 3 2 Ha: state the p-value= State Conclusions, i.e. what can we conclude regarding the hypothe 3 4 4 3 4 4 2 5 3 4 2 3 ting in cell F4) de regarding the hypothesis statement (based upon significance level of 0.05) Designers of backpacks use exotic material such as supernylon Delrin, high-density ethylene, aircraft aluminum, and thermo molded floam to make packs that fit comfortably and distribute weight to eliminate pressure points. The following data show the capacity (cubic inches), comfort rating, and price (dollars) for 10 backpacks tested by Outside Magazine. Comfort was measured using a rating from 1 to 5, with a rating of 1 denoting average comfort and a rating of 5 denoting excellent comfort. Run a regression of price on comfort and capacity using Excel (data is given on the adjacent worksheet) and then answer the following questions. Make sure to generate a proper Residual Plot (residuals versus 'predicted-y') as well as a proper Normal Probability Plot for this regression. 1. What is the interpretation of adjusted R-square for this problem? 2. What price would you predict for a backpack with a mean capacity of 4700 (cubic inches) and comfort rating of 3? (show equation and values used) 3. Provide the appropriate test statistic and p-value for assessing whether there is statisical evidence (i.e. statistical significance) that comfort aids in predicting price. 4. Provide an interpretation for the estimated regression coefficient of capacity. On average, all else being equal, for each cubic inch increase in capacity, the price of the backpack decreases by $0.094 (or 9.4 cents). 5. Is the overall model significant at 0.05 level of significance? Why or Why not. 6. Does capacity aid in predicting price at 0.05 level of significance (i.e. is the coefficient statistcally significant at 0.05)? Why or Why not. 7. What is the 90% confidence interval for the estimated regression coefficient of comfort? Manufacturer and Model Marmot Muir Gregory Whitney Osprey 75 Lowe Alpomayo 90+20 Arc'Teryx Bora 95 The Works @ Mystery Ranch Jazz EMS 5500 Dana Design Terraplane LTW Camp Trails Paragon II Kelly Bigfoot 5200 Capacity Comfort Price 4700 5500 4700 5500 5300 5000 5500 5800 4330 5200 3 4 4 4 4 5 3 5 2 4 249 340 389 249 395 525 219 439 190 250 Place the regression output starting cell F2 below
