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. $$\begin{array} { r | c c }
& \text { Correct } & \text { Incorrect } \
\hline \text { Math } & 27 & 53 \
\text { English } & 43 & 37
\end{array}$$ $x ^ { 2 }$ = 6.502; P-value = 0.011 Are the response and major independent? Use a 5% level of significance.
A)Report that the distribution of correct answers is uniform for both majors because the null hypothesis is rejected.
B)Report that response is not dependent on major because the null hypothesis is rejected.
C)Report that response is not dependent on major because the null hypothesis is not rejected.
D)Report that response is dependent on major because the null hypothesis is rejected.
E)Report that response is dependent on major because the null hypothesis is not rejected.

Question

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. $$\begin{array} { r | c c } 
& \text { Correct } & \text { Incorrect } \
\hline \text { Math } & 27 & 53 \
\text { English } & 43 & 37
\end{array}$$ $x ^ { 2 }$ = 6.502; P-value = 0.011 Are the response and major independent? Use a 5% level of significance.
A)Report that the distribution of correct answers is uniform for both majors because the null hypothesis is rejected.
B)Report that response is not dependent on major because the null hypothesis is rejected.
C)Report that response is not dependent on major because the null hypothesis is not rejected.
D)Report that response is dependent on major because the null hypothesis is rejected.
E)Report that response is dependent on major because the null hypothesis is not rejected.

Quizplus · Accepted Answer

The null hypothesis in this case is that the response (correct/incorrect) is independent of the major (math/English). Since the P-value is less than the significance level of 5%, we reject the null hypothesis. This means that we have evidence to suggest that there is a relationship between the response and major, and therefore the response is dependent on major. Choice D is the statement that reflects this conclusion.

160 Students Who Were Majoring in Either Math or English Correct Incorrect Math 2753 English 4337\begin{array} { r | c c } & \text { Correct } & \text { Incorrect } \\\hline \text { Math } & 27 & 53 \\\text { English } & 43 & 37\end{array} Math English ​ Correct 2743​ Incorrect 5337​​

160 Students Who Were Majoring in Either Math or English $\begin{array} { r | c c } & \text { Correct } & \text { Incorrect } \\\hline \text { Math } & 27 & 53 \\\text { English } & 43 & 37\end{array}$