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. This table lists the results of the study. At $= .05$, test the claim that the rodent type and the success of finishing the maze are not related $\begin{array}{lcc} & \text { Mice } & \text { Rats } \ \text { Finished } & 22 & 27 \ \text { Did not Finish } & 26 & 16 \end{array}$ 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 $3.841 2.624$ 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 $9.488 1.365$ C) There is not evidence to reject the claim that the rodent type and the success of finishing the maze are . not related because the test value $2.624

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. This table lists the results of the study. At $= .05$, test the claim that the rodent type and the success of finishing the maze are not related $\begin{array}{lcc} & \text { Mice } & \text { Rats } \ \text { Finished } & 22 & 27 \ \text { Did not Finish } & 26 & 16 \end{array}$ 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 $3.841 > 2.624$ 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 $9.488 > 1.365$ C) There is not evidence to reject the claim that the rodent type and the success of finishing the maze are . not related because the test value $2.624 < 3.841$ D)There is not evidence to reject the claim that the rodent type and the success of finishing the maze are . not related because the test value $1.365 < 9.488$

Quizplus · Accepted Answer

We need to perform a chi-square test of independence. The null hypothesis is that the rodent type and the success of finishing the maze are not related, and the alternative hypothesis is that they are related. We can set up the expected values for each cell under the assumption that the null hypothesis is true:

$\begin{array}{lcc} 
& \text { Mice } & \text { Rats } & \text{Total} \
\text { Finished } & 24.8 & 24.2 & 49 \
\text { Did not Finish } & 23.2 & 22.8 & 46 \
\text{Total} & 48 & 47 & 95
\end{array}$

We can then calculate the chi-square test statistic as:

$\chi^2 = \sum \frac{(observed - expected)^2}{expected}$

Plugging in the observed and expected values, we get:

$\chi^2 = \frac{(22-24.8)^2}{24.8} + \frac{(27-24.2)^2}{24.2} + \frac{(26-23.2)^2}{23.2} + \frac{(16-22.8)^2}{22.8} = 2.624$

To determine whether this value is statistically significant, we need to compare it to the critical value from the chi-square distribution with 1 degree of freedom (since we have one categorical variable with two levels). At the 0.05 level of significance, the critical value is 3.841. Since our test value of 2.624 is less than the critical value of 3.841, we do not have enough evidence to reject the null hypothesis. Therefore, we can conclude that there is not evidence to reject the claim that the rodent type and the success of finishing the maze are not related.

A Biologist Had Mice and Rats Run Through a Maze =.05= .05=.05

A Biologist Had Mice and Rats Run Through a Maze $= .05$