AP Statistics 8.3 Carrying Out a Chi-Square Test for Goodness of Fit - MCQs - Exam Style Questions

The appropriate test is a chi-squared ($\chi^2$) goodness-of-fit test. The contribution of each category to the test statistic is calculated as:
Contribution = $\frac{(\text{Observed} – \text{Expected})^2}{\text{Expected}}$

1. Calculate Expected Counts:
The total sample size is $n=200$. Expected = $n \times$ Proportion.
– Beef: $200 \times 0.18 = 36$
– Chicken: $200 \times 0.41 = 82$
– Fish: $200 \times 0.15 = 30$
– Pork: $200 \times 0.20 = 40$
– Vegetarian: $200 \times 0.06 = 12$

2. Calculate Contribution for Each Dinner Type:
– Beef: $\frac{(32-36)^2}{36} = \frac{16}{36} \approx 0.44$
– Chicken: $\frac{(86-82)^2}{82} = \frac{16}{82} \approx 0.20$
– Fish: $\frac{(34-30)^2}{30} = \frac{16}{30} \approx 0.53$
– Pork: $\frac{(30-40)^2}{40} = \frac{100}{40} = 2.50$
– Vegetarian: $\frac{(18-12)^2}{12} = \frac{36}{12} = 3.00$

The largest contribution value is 3.00, from the Vegetarian category.
✅ Answer: (E)