Consider a situation in which we expect the same frequency of 64 total observations to be in each of four categories. We can use an ?² goodness-of-fit test to test whether the frequencies of offspring are as expected. If the numbers of values in each category are 12, 26, 8, and 18, and using the table of critical values shown, what is the conclusion of our test?
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$\begin{array}{c}\chi^{2} \text { critical values }\\\text { for } d f=2\\\begin{array}{ll}\text { Sig. level } & \text { Value } \\\hline 0.05 & 7.81\\0.025 & 9.35 \\0.01 & 11.34\end{array}\end{array}$

Question

Consider a situation in which we expect the same frequency of 64 total observations to be in each of four categories. We can use an ?² goodness-of-fit test to test whether the frequencies of offspring are as expected. If the numbers of values in each category are 12, 26, 8, and 18, and using the table of critical values shown, what is the conclusion of 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 & 7.81\\0.025 & 9.35 \\0.01 & 11.34\end{array}\end{array}

Quizplus · Accepted Answer

Given the expected frequency of 16 in each category (64 total observations divided by 4 categories), we calculate the chi-square statistic using the observed frequencies (12, 26, 8, and 18). The calculation would show a significant difference from the expected frequencies, leading to the rejection of the null hypothesis. The provided critical values table and degrees of freedom (df) are not directly applicable since the df for a chi-square goodness-of-fit test with four categories is 3 (n-1), not 2 as shown. However, the conclusion to reject the null hypothesis is based on the premise of significant deviation from expected frequencies, not the specific critical values provided.

Consider a Situation in Which We Expect the Same Frequency