A biologist had mice and rats run through a maze and recorded the number that finished the maze successfully and the number that did not. The table lists the results of the study. At $\alpha = 0.05$, test the claim that the rodent type and the success of finishing the maze are nc related. $\begin{array} { l c c } & \text { Mice } & \text { Rats } \ \text { Finished } & 22 & 28 \ \text { Did not Finish } & 30 & 11 \end{array}$ A) There is evidence to reject the claim that the rodent type and the success of finishing the maze are not related because the test value 3.841 3.841 C) There is evidence to reject the claim that the rodent type and the success of finishing the maze are not related because the test value 2.382 2.382

Question

A biologist had mice and rats run through a maze and recorded the number that finished the maze successfully and the number that did not. The table lists the results of the study. At $\alpha = 0.05$, test the claim that the rodent type and the success of finishing the maze are nc related. $\begin{array} { l c c } & \text { Mice } & \text { Rats } \ \text { Finished } & 22 & 28 \ \text { Did not Finish } & 30 & 11 \end{array}$ A) There is evidence to reject the claim that the rodent type and the success of finishing the maze are not related because the test value 3.841 < 7.827 B) There is evidence to reject the claim that the rodent type and the success of finishing the maze are not related because the test value 7.827 > 3.841 C) There is evidence to reject the claim that the rodent type and the success of finishing the maze are not related because the test value 2.382 < 9.488 D) There is evidence to reject the claim that the rodent type and the success of finishing the maze are not related because the test value 9.488 > 2.382

Quizplus · Accepted Answer

The correct choice is based on a chi-square test for independence. The calculated chi-square value (7.827) is compared against the critical value from the chi-square distribution table at $\alpha = 0.05$ for the appropriate degrees of freedom (usually 1 for a 2x2 table like this), which is 3.841. Since 7.827 > 3.841, we reject the null hypothesis, indicating that there is a statistically significant association between rodent type and success in finishing the maze.

A Biologist Had Mice and Rats Run Through a Maze α=0.05\alpha = 0.05α=0.05

A Biologist Had Mice and Rats Run Through a Maze $\alpha = 0.05$