Consider a Situation in Which We Expect One-Third of the Observed

Multiple Choice

Consider a situation in which we expect one-third of the observed values to be in each of 3 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 14, 19, and 27, and using the table of critical values shown, what is the conclusion of our test?
?
$\begin{array}{c}\chi^{2} \text { critical values }\\\text { for } d f=2\\\begin{array}{ll}\text { Sig. level } & \text { Value } \\\hline 0.05 & 5.99 \\0.025 & 7.38 \\0.01 & 9.21\end{array}\end{array}$

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.