Chi-Square Goodness-of-Fit Test
The table shows the observed counts for meal preferences from a survey of 300 students. A chi-square goodness-of-fit test is conducted to determine if the sample distribution is consistent with the expected proportions: 20% vegetarian, 30% vegan, and 50% omnivorous. What are the chi-square statistic and the correct conclusion at the 0.05 significance level, given a critical value of for 2 degrees of freedom?
| Meal Option | Observed Count | Expected Proportion |
|---|---|---|
| Vegetarian | 70 | 20% |
| Vegan | 90 | 30% |
| Omnivorous | 140 | 50% |
| Total | 300 | 100% |
The chi-square statistic is approximately ; therefore, we reject the null hypothesis as the deviation is significant.
The chi-square statistic is approximately , which exactly meets the threshold for rejection.
The chi-square statistic is approximately ; since this is less than , there is insufficient evidence to reject the null hypothesis.
The chi-square statistic is approximately ; thus, we conclude that the observed distribution significantly deviates from the expected distribution.
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