Consider a Situation in Which We Expect the Same Frequency

Multiple Choice

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, 24, 10, and 18, and using the table of critical values shown, what is the conclusion of our test?
?
$\begin{array}{c}\chi^{2} \text { critical values }\\\text { for } d f=2\\\begin{array}{ll}\text { Sig. level } & \text { Value } \\\hline 0.05 & 7.81\\0.025 & 9.35 \\0.01 & 11.34\end{array}\end{array}$

A) Fail to reject the null hypothesis, we lack the evidence to decide that the frequencies differ from those that were expected.
B) Fail to reject the null hypothesis, we have good evidence to decide that the frequencies differ from those that were expected.
C) Reject the null hypothesis, we lack the evidence to decide that the frequencies differ from those that were expected.
D) Reject the null hypothesis, we have good evidence to decide that the frequencies differ from those that were expected.