APFIVE A college cafeteria survey of 300 respondents presents the observed meal preference counts in the table above. The theoretical expectation is that 20% of students choose vegetarian, 30% choose vegan, and 50% choose omnivorous meals. Calculate the chi-square statistic for this goodness-of-fit test and determine the conclusion at the 0.05 significance level (the critical value for df = 2 is approximately $$5.991$$).
| Meal Option | Observed Count | Expected Proportion |
|---|---|---|
| Vegetarian | 70 | 20% |
| Vegan | 90 | 30% |
| Omnivorous | 140 | 50% |
| Total | 300 | 100% |
The chi-square statistic is approximately $$2.33$$; therefore, we reject the null hypothesis as the deviation is significant.
The chi-square statistic is approximately $$10.00$$; thus, we conclude that the observed distribution significantly deviates from the expected distribution.
The chi-square statistic is approximately $$2.33$$; since this is less than $$5.991$$, there is insufficient evidence to reject the null hypothesis.
The chi-square statistic is approximately $$5.99$$, which exactly meets the threshold for rejection.
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