A market researcher wanted to test three exotic flavors of cake (dragon fruit, root beer, and yam) on customers of different age groups (21-30, 31-40, 41-50, 51-60). Thus, age is a blocking variable. The dependent measure was the customer's rating on how much he/she liked the cake. There were six subjects in each cell. Complete the ANOVA summary table below, assuming a fixed-effects model where $\alpha$ = .05.

$\begin{array}{cccccccc}
\hline \text { Source } & S S & d f & M S & F & \text { Critical Value } & \text { Decision } \
\hline \text { Flavor }(\mathrm{A}) & 300 & - & - & - & - & - \
\text { Age }(\mathrm{B}) & - & - & 50 & - & - & - \
\text { Interaction }(\mathrm{AB}) & - & - & - & - & - & - \
\text { Within } & - & - & 25 & & & - \
\text { Total } & 2400 & - & & & & \
\hline
\end{array}$

Question

A market researcher wanted to test three exotic flavors of cake (dragon fruit, root beer, and yam) on customers of different age groups (21-30, 31-40, 41-50, 51-60). Thus, age is a blocking variable. The dependent measure was the customer's rating on how much he/she liked the cake. There were six subjects in each cell. Complete the ANOVA summary table below, assuming a fixed-effects model where $\alpha$ = .05.

$\begin{array}{cccccccc}
\hline \text { Source } & S S & d f & M S & F & \text { Critical Value } & \text { Decision } \
\hline \text { Flavor }(\mathrm{A}) & 300 & - & - & - & - & - \
\text { Age }(\mathrm{B}) & - & - & 50 & - & - & - \
\text { Interaction }(\mathrm{AB}) & - & - & - & - & - & - \
\text { Within } & - & - & 25 & & & - \
\text { Total } & 2400 & - & & & & \
\hline
\end{array}$

Quizplus · Accepted Answer

The Answer is There are 3 levels of the fixed factor A (flavors of cake), so J = 3. There are 4 levels of the fixed factor B (age), so K = 4. Each cell has 6 subjects, so n = 6. N = 6*3*4 = 72.

df_A= J -1 = 3 - 1 = 2, df_B = K - 1 = 4 -1 = 3, df_A_B = (J - 1)(K - 1) = 2*3 = 6, df_with = N - JK = 72 - 3*4 = 60, df_total = N - 1 = 72 - 1 = 71.

SS_B = MS_B*df_B = 50*3 = 150; SS_with = MS_with*df_with = 25*60 = 1500;
SS_with = SS_total - SS_A ? SS_B- SS_with = 2400 - 300 - 150 - 1500 = 450.

MS_A = SS_A/df_A = 300/2 = 150; MS_AB = SS_AB /df_AB = 450/6 = 75.

F_A = MS_A/MS_with = 150/25 = 6; critical value for A = _.0₅F₂_,₆₀ = 3.15 < F_A, reject H₀.
F_B = MS_B/MS_with = 50/25 = 2; critical value for B = _.0₅F_3,60 = 2.76 > F_B, fail to reject H₀.

F_A_B = MS_AB/MS_with = 75/25 = 3; critical value for AB= _.0₅F_6,60 = 2.25 < F_AB, reject H₀.

\begin{array}{ccccccc}\hline ext { Source } & S S & d f & M S & F & ext { Critical Vahe } & ext { Decision } \\hline ext { Flavor }(\mathrm{A}) & 300 & 2 & 150 & 6 & .05 F_{2,60}=3.15 & ext { reject } H_{0} \ ext { Age }(\mathrm{B}) & 150 & 3 & 50 & 2 & .05 F_{3,60}=2.76 & ext { fail to reject } H_{0} \ ext { Interaction }(\mathrm{AB}) & 450 & 6 & 75 & 3 & .05 F_{6,60}=2.25 & ext { reject } H 0 \ ext { Within } & 1500 & 60 & 25 & & & \ ext { Total } & 2400 & 71 & & & & \\hline\end{array}

A Market Researcher Wanted to Test Three Exotic Flavors of Cake