Consider a claim that 60% of the mice in a region have parasitic infections. We can use an ?² 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 36 have infections. Calculate the ?²value, and using the table of critical values shown, what is the P-value range we would obtain for our test?
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$\begin{array}{c}\chi^{2} \text { critical values }\\\text { for } d f=2\\\begin{array}{ll}\text { Sig. level } & \text { Value } \\\hline 0.05 & 3.84 \\0.025 & 5.02 \\0.01 & 6.63\end{array}\end{array}$

Question

Consider a claim that 60% of the mice in a region have parasitic infections. We can use an ?² 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 36 have infections. Calculate the ?²value, and using the table of critical values shown, what is the P-value range we would obtain for our test?
?

\begin{array}{c}\chi^{2} \text { critical values }\\\text { for } d f=2\\\begin{array}{ll}\text { Sig. level } & \text { Value } \\\hline 0.05 & 3.84 \\0.025 & 5.02 \\0.01 & 6.63\end{array}\end{array}

Quizplus · Accepted Answer

The chi-square test 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 this scenario, we expect 60% of the 50 mice to have infections, which is 30 mice. The observed number is 36. So, the calculation is $\chi^2 = \frac{(36-30)^2}{30} + \frac{(14-20)^2}{20} = 3$. Since the chi-square value is not provided in the question, we cannot calculate it directly, but we use the critical values table for interpretation. If the calculated chi-square value were less than 3.84, the P-value would be greater than 0.05, indicating that the difference between observed and expected frequencies is not statistically significant at the 0.05 level.

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