Question

Math

Posted 4 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
\end{tabular}
$\begin{array}{l}
\chi^{2}=5.19, \mathrm{DF}=2 \\
\text { P-value }=0.075
\end{array}$
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 4 months ago

Solution by Steps

step 2

The 'Components' values given are 0.06 for pork, 2 for chicken, and 3.13 for vegetarian

step 3

The type of ramen with the highest 'Components' value contributed the most to the chi-square test statistic

step 4

Vegetarian ramen has the highest 'Components' value of 3.13

step 5

Therefore, vegetarian ramen contributed the most to the chi-square test statistic

[question number] Answer

C

Key Concept

Chi-square test statistic contribution

Explanation

The type of ramen that contributes the most to the chi-square test statistic is the one with the highest 'Components' value in the chi-square table.

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