A company markets its products by direct mail. An experiment was conducted to study the effects on customer response rat

[answerhappygod]

A Company Markets Its Products By Direct Mail An Experiment Was Conducted To Study The Effects On Customer Response Rat 1 (86.11 KiB) Viewed 49 times

A Company Markets Its Products By Direct Mail An Experiment Was Conducted To Study The Effects On Customer Response Rat 2 (59.09 KiB) Viewed 49 times

A company markets its products by direct mail. An experiment was conducted to study the effects on customer response rate of the offered price (labelled as A) and type of mail (labelled as B). There are many different levels of offered prices so 2 price levels were selected at random for the study: $20.00 (labelled as - ) and $30.00 (labelled as +). The company only uses 2 types of mail: 2nd class (labelled as -) and 1 * class (labelled as +). The mailings are made to three groups of customers. The number of orders received is recorded in the table below. Factor A B Replicates II I III 50 Treatment Combination (1) al b. ab 54 56 42 46 47 43 48 + + Total 160 134 139 139 49 45 48 + i) Identify the experimental design being performed. ii) Derive, from first principles, an expression for the estimate of the effect of B. Calculate this estimate. iii) Using the table above, compute estimates for the sum of squares of effect A and the sum of squares of the interaction effect AB. The data given is then analyzed in the statistical software R and the following output generated where some information is removed.

Orders = c(50,54,56,42,43,49,46, 48, 45, 47, 44,48) > model = lm (Orders AB) > anova (model) Analysis of Variance Table Response: Orders DE Sum Sa A 1 *REMOVED* B 1 21.333 A:B 1 *REMOVED* Residuals 8 60.667 Mean Sq *REMOVED* 21.333 *REMOVED* 7.583 F value * REMOVED* 2.8132 *REMOVED* Pr(>F) *REMOVED* *REMOVED* *REMOVED* iv) Which effects in the table above (A, B, AB, Residuals) are fixed and which are random? v) Using the table of expected means provided on page 9, find the F value for the variable A. What hypotheses does this F value test? Test these hypotheses at a = 0.10. vi) Using the table of expected means provided, find the F value for variable B. What hypotheses does this value test? Test these hypotheses at a = 0.10. vii) Using the output above and the table of Expected Mean Squares, find Analysis-of-Variance estimates for the variance components for any random effects in the model. [1 +3+4+2+4+4+5]