Consider a claim that 60% of the mice in a region have parasitic infections. We can use an χ² goodness-of-fit test to test whether the proportion is indeed 60%. Consider a study in which we collect a random sample of 50 mice and 37 have infections. What is the χ²value we would obtain?

Question

Quizplus · Accepted Answer

The chi-square value is calculated using the formula: $\chi^2 = \sum \frac{(O_i - E_i)^2}{E_i}$, where $O_i$ is the observed frequency and $E_i$ is the expected frequency. For the infected mice, $O_i = 37$ and $E_i = 50 \times 0.60 = 30$. For the non-infected mice, $O_i = 13$ and $E_i = 50 \times 0.40 = 20$. Plugging these into the formula gives $\chi^2 = \frac{(37-30)^2}{30} + \frac{(13-20)^2}{20} = \frac{49}{30} + \frac{49}{20} = 4.083$.

Consider a Claim That 60% of the Mice in a Region