A market researcher wanted to know whether different package designs for the same yogurt product would affect consumers' purchase intention. There were four different versions of package designs. Each package was viewed by eight participants, who then rated their likelihood to purchase the product. A one-factor ANCOVA was used to analyze the data where the covariate was the participants' liking of the yogurt product in general. Complete the following ANCOVA summary table ($\alpha$ = .05):

$\begin{array}{ccccccc}
\text { Source } & S S & d f & M S & F & \text { Critical Value } & \text { Decision } \
\hline \text { Between adjusted } & 10.5 & - & - & - & - & - \
\text { Within adjusted } & - & - & - & - & - & - \
\text { Covariate } & \overline{35} & - & 5.6 & - & - & - \
\text { Total } & - & & & - & \
\hline
\end{array}$

Question

A market researcher wanted to know whether different package designs for the same yogurt product would affect consumers' purchase intention. There were four different versions of package designs. Each package was viewed by eight participants, who then rated their likelihood to purchase the product. A one-factor ANCOVA was used to analyze the data where the covariate was the participants' liking of the yogurt product in general. Complete the following ANCOVA summary table ($\alpha$ = .05):

$\begin{array}{ccccccc}
\text { Source } & S S & d f & M S & F & \text { Critical Value } & \text { Decision } \
\hline \text { Between adjusted } & 10.5 & - & - & - & - & - \
\text { Within adjusted } & - & - & - & - & - & - \
\text { Covariate } & \overline{35} & - & 5.6 & - & - & - \
\text { Total } & - & & & - & \
\hline
\end{array}$

Quizplus · Accepted Answer

The Answer is The factor (designs of cereal packages) has 4 levels, so J = 4. Each level has 8 participants, so n = 8, N = 4*8 = 32.
There is one covariate (liking of yogurt).
df_betw₍_adj₎= J - 1 = 4 - 1 = 3, df_with₍_adj₎ = N - J - 1 = 32 - 4 - 1 = 27, df_cov = 1,df_total = N - 1 = 32- 1 = 31.

SS_cov= df_cov*MS_cov = 1*5.6 = 5.6,
SS_with₍_adj₎ = SS_total -SS_betw₍_adj₎ -SS_cov = 35 - 10.5 ? 5.6 = 18.9.

MS_betw₍_adj₎ = SS_betw₍_adj₎/df_betw₍_adj₎ = 10.5/3 = 3.5.

MS_with₍_adj₎ = SS_with₍_adj₎/df_with₍_adj₎ = 18.9/27 = 0.7.

F_betw₍_adj₎= MS_betw₍_adj₎/MS_with₍_adj₎= 3.5/0.7 = 5; critical value = _.05F_3,27= 2.96 < F_betw₍_adj₎, reject H₀.

F_cov = MS_cov/MS_with_(adj) = 5.6/0.7 = 8; critical value = _.05F₁_,₂₇ = 4.21 < F_cov, reject H₀.

\begin{array}{crrrrrr} ext { Source } & S S & \boldsymbol{d f} & \boldsymbol{M S} & \boldsymbol{F} & ext { Critical Value } & ext { Decision } \\hline ext { Between adjusted } & 10.5 & 3 & 3.5 & 5 & 05 F_{3,27}=2.96 & ext { Reject } H 0 \ ext { Within adjusted } & 18.9 & 27 & 0.7 & & & \ ext { Covariate } & 5.6 & 1 & 5.6 & 8 & .05 F_{1,27}=4.21 & ext { Reject } H_{0} \ ext { Total } & 35.0 & 31 & & & & \\hline\end{array}

A Market Researcher Wanted to Know Whether Different Package Designs α\alphaα

A Market Researcher Wanted to Know Whether Different Package Designs $\alpha$