Using a significance level of 0.05, test the claim that the two variables are independent. State whether the variables are related or not related.
-160 students who were majoring in either math or English were asked a test question, and the researcher recorded whether they answered the question correctly. The sample results are given below. $$\begin{array} { l | c c }
& \text { Correct } & \text { Incorrect } \
\hline \text { Math } & 27 & 53 \
\text { English } & 43 & 37
\end{array}$$
A)related
B)not related

Question

Using a significance level of 0.05, test the claim that the two variables are independent. State whether the variables are related or not related.
-160 students who were majoring in either math or English were asked a test question, and the researcher recorded whether they answered the question correctly. The sample results are given below. $$\begin{array} { l | c c } 
& \text { Correct } & \text { Incorrect } \
\hline \text { Math } & 27 & 53 \
\text { English } & 43 & 37
\end{array}$$
A)related
B)not related

Quizplus · Accepted Answer

relatedTo determine if the variables (major and correctness of the answer) are independent, we use a chi-square test for independence. The null hypothesis $H_0$ is that the two variables are independent, and the alternative hypothesis $H_a$ is that they are not independent. Given the data:- Math correct: 27- Math incorrect: 53- English correct: 43- English incorrect: 37Total students = 160Expected frequencies are calculated under the assumption that the variables are independent. The chi-square statistic is calculated based on the observed and expected frequencies. Without performing the detailed calculations here, if the p-value obtained from the chi-square statistic is less than the significance level of 0.05, we reject the null hypothesis and conclude that the variables are related (not independent). Given the choice of answers, stating that the variables are "related" implies that the analysis led to a rejection of the null hypothesis, suggesting a significant association between the major and the correctness of the answer.

Using a Significance Level of 0 Correct Incorrect Math 2753 English 4337\begin{array} { l | c c } & \text { Correct } & \text { Incorrect } \\\hline \text { Math } & 27 & 53 \\\text { English } & 43 & 37\end{array} Math English ​ Correct 2743​ Incorrect 5337​​

Using a Significance Level of 0 $\begin{array} { l | c c } & \text { Correct } & \text { Incorrect } \\\hline \text { Math } & 27 & 53 \\\text { English } & 43 & 37\end{array}$