Question

Math

Posted 6 months ago

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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
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Answer from Sia

Posted 6 months ago

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 $3.13$.

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