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A consumer preterence study compares the effects of three different bottle designs (A, B, and C) on sales of a popular fabric sortener. A completely randomized design is employed. Specifically, 15 supermarkets of equal sales potential are selected, and 5 of these supermarkets are randomly assigned to each bottle design. The number of bottles sold in 24 hours at each supermarket is recorded. The data obtained are displayed in the tollowing table Bottle Design Study Data 15 13 18 16 19 32 26 21 25 30 32 The Excel output of a one-way ANOVA of the Bottle Design Study Data is shon below. SUMMA Count Sum Average Variance Design A Design B Design C 81 157 124 16.2 31.1 24.8 5.7 1.8 Source of Variation Bctween Grouos Within Groups Total P.Value 3.23E-D6 38529 F crit 290.4567 5.0557 530.9333 57.33 608 12.0 641.1333 14 (a) Test the null hypothesis that PA MB, and uc are equal by setting 05. Based on this test, can we conclude that bottle designs A, B, and C have different effects on mean daily sales? (Round your answers to 2 decimal places. Leave no cells blank be certain to entero wherever required.) 7 33 0.00 p-value Do not reject ▼ | His bottle design does have an impact on sales.onsider the pair se differences μ Ha A and μ B-Find a oint estimate or and a Tukey simultaneous 95 er en confidence interval t reac se difference er et esult in tica e s.wh Which bottle design maximizes mean daily sales? (Round your answers to 2 decimal places. Negative amounts should be indicated by a minus sign.) Point estimate Confidence interva Bottle design B maximizes sales c Find a 95 percent confidence Interval for each of the treatment means μ4 Ha and μο-Interpret these intervals Round your answers to 2 decimal places. Negative amounts should be Indicated by a minus sign. Confidence interval HA Us

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b)

Tukey HSD Qcrit value-377 at α= 5%,k = 3 and d. = 60.8 The 95% confidence interval between /4 and 2 is (-)314-162)+13.146 (2 053561 2834643921) There is significance difference between the means of column 1 and column 2 The 95% confidence interval between A4 and 3 is (n-n)±ME-(24.8-162)±13.146 =(4546439, 2174643921) There is no significance difference between the means of column 1 and column 3 The 95% confidence interval between μ2 and 14, is (-3-n) IE-(24.8-31.4) 13.146-(-1974644, 6546439214) There is no significance difference between the means of column 2 and column 3

c)

Marginal Error-t i,(d)xy2MS./ n-2. 1788V2#60.8 / 5 10.74488 he 95% confidence interval among the means are X1-X2)±ME = (16.2-31.4)±10.74488-(4.455116546 25.94488345) Yhere is significance difference between the means of group 1 and group 2 (n-5)±ME = (24.8-16.2)±10.74488-(-2.14488345 19.34488345) There is no significance difference between the means of group 2 and group 3 (h-%)±ME =(24.8-31.4)±1074488 =(-17.3448835 4.144883454) There is no significance difference between the means of group 1 and grouj

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