Salma operates a ramen restaurant. Historically, half of customers order pork ramen, and the other half of customers are split evenly between chicken and vegetarian ramen. Salma modified the chicken and vegetarian recipes, and she wonders if customers' ordering habits will change. Here are results from a sample of 32 orders after launching the new recipes along with a chi-square goodness-of-fit test:
\begin{tabular}{lrrr}
Type of ramen & Pork & Chicken & Vegetarian \
\hline Historical distribution & $50 \%$ & $25 \%$ & $25 \%$ \
Observed & 15 & 4 & 13 \
Expected & 16 & 8 & 8 \
Components & 0.06 & 2 & 3.13 \
$\chi^{2}=5.19, \mathrm{DF}=2$ & & & \
P-value $=0.075$ & & &
\end{tabular}

Which type of ramen contributed the most to the test statistic?
Choose 1 answer:
(A) Pork ramen
(B) Chicken ramen
(C) Vegetarian ramen

Question

Salma operates a ramen restaurant. Historically, half of customers order pork ramen, and the other half of customers are split evenly between chicken and vegetarian ramen. Salma modified the chicken and vegetarian recipes, and she wonders if customers' ordering habits will change. Here are results from a sample of 32 orders after launching the new recipes along with a chi-square goodness-of-fit test:
\begin{tabular}{lrrr} 
Type of ramen & Pork & Chicken & Vegetarian \
\hline Historical distribution & $50 \%$ & $25 \%$ & $25 \%$ \
Observed & 15 & 4 & 13 \
Expected & 16 & 8 & 8 \
Components & 0.06 & 2 & 3.13 \
$\chi^{2}=5.19, \mathrm{DF}=2$ & & & \
P-value $=0.075$ & & &
\end{tabular}

Which type of ramen contributed the most to the test statistic?
Choose 1 answer:
(A) Pork ramen
(B) Chicken ramen
(C) Vegetarian ramen

Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ Identify the component for each type of ramen from the table. ‖ ‖ step 2 ⋮ The components are calculated using the formula $\frac{(O - E)^2}{E}$, where $O$ is the observed value and $E$ is the expected value. ‖ ‖ step 3 ⋮ Compare the components for pork, chicken, and vegetarian ramen to determine which is the largest. ‖ ‖ step 4 ⋮ The component for pork ramen is $0.06$, for chicken ramen is $2$, and for vegetarian ramen is $3.13$. ‖ ‖ step 5 ⋮ The largest component is for vegetarian ramen, which is $3.13$. ‖ ∻1 Answer∻ ⚹ (C) Vegetarian ramen ⚹ ∻Key Concept∻ ⚹Chi-square component contribution⚹ ∻Explanation∻ ⚹The type of ramen that contributed the most to the chi-square test statistic is the one with the largest component in the chi-square calculation. In this case, it is the vegetarian ramen with a component of $3.13$.⚹◊What is the formula for calculating the chi-square goodness-of-fit test statistic in this scenario?⍭ Generate me a similar question◊

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