1|]. Two-factor analysis of variance Permissionbased email marketing is the tactic of marketing one's products and services through email but with the recipient's permission. This is in contrast to spamming, which is done without regard for the recipient's wishes. An industry expert offered the following advice to permission-based e-mail marketers: \"The rst keg.r is to make your efforts more subscriber-centric and permission veried . . . The second key is to test, test, test. Email is so costeffecve, measurable, and immediate, that it is the perfect medium to improve through testing.\" [Source: Keves, Whitney M. \"Exact Target Shares Tip on E-Mail Marketing.\" Seattle Post-Intelligencer, June 25, 2008.] Heeding this advice, an email marketer conducted a factorial experiment to test the effecveness of two factors in generating sales. The rst factor, called Factor A, consists of three different subject lines for the email message. 111e second factor, called Factor B, is whether the email message includes an mazoncom voucher that the recipient can redeem if a purchase is made. The experimental units are batches of 20,000 e-mail addresses obtained from the marketer's database. E-mail messages, adjusted according to the factor levels, are sent to all the addresses in each batchr and the total sales amount for each batch is recorded as a measure of response. The results of the study are summarized by the corresponding sample means in the table that follows. All gures are in dollars. Dam Summarwr Factor B: Voucher No Voucher Factor A Sample Means Faclaor A: Subject line 1 192.50 130.10 161.30 Subject Line 2 208.20 159.00 183.60 Subject line 3 183.10 121.00 152.05 Factor B Sample Mea ns 1 94 .60 13 6.?0 The number of replications for each cell of the table is 5. Thus, the number of observations is Use the information in the previous table to answer the following question. The total sales amount for the units assigned e-mail messages with Subject Line 2 and no voucher is . The average sales amount for units assigned e-mail messages with Subject Line 2 is . The average sales amount for units assigned e-mail messages with no voucher is . The overall sample mean response for the experiment is The investigator performed an analysis of variance (ANOVA) to test the hypothesis that the populations defined by the treatment combinations are equal. You would like to determine the presence of main effects due to Factors A and B, respectively, and the interaction effect of both. Some of the results are presented in the following table. ANOVA Table Source of Variation Sum of Squares Degrees of Freedom Mean Square F p value Factor A 2,630.40 1.799 0.1871 Factor B 25,143.15 17.192 0.0004 Interaction 283.90 0.9079 Error Total 65,786.84 29Please go through the following steps to complete the ANDVA table just given. 1. The sum of squared deviations of the Factor A sample means from the overall sample mean is 526.08. The sum of squared deviations of the Factor B sample means from the overall sample mean is 1,6?6.21. Select the appropriate value for the sums of squares for Factors A and B in the ANDVA table. 2. Select the appropriate value for the sum of squares due to error in the ANOVA table. 3. Select the appropriate degrees of freedom for all the sums of squares in the ANDWI table. II. Select the appropriate values for the mean square due to interaction, the mean square due to errorI and the F statistic for the interaction effect. Use the results from the completed ANOVA table to make the following conclusions. At the signicance level of o = 0.05, the main effect due to Factor A is v , the main effect due to Factor Bis v , and the interaction effect of the two factors is V . According to the order of testing in the two-factor ANDVA, in this situation the F-tests for the presence of main effects due to factors A and B V conducted