Instruction 15-7
According to an article in Marketing News, fewer cheques are being written at grocery store checkout stands than in the past. To determine whether there is a difference in the proportion of shoppers who pay by cheque among three consecutive years at a 0.05 level of significance, the results of a survey of 500 shoppers in three consecutive years are obtained and presented below.
$$\begin{array} { | l | c | c | c | }
\hline \text { Cheque Written } & \text { Year 1 } & \text { Year 2 } & \text { Year 3 } \
\hline \text { Yes } & 225 & 175 & 125 \
\hline \text { No } & 275 & 175 & 125 \
\hline
\end{array}$$
-Referring to Instruction 15-7,what is the correct conclusion?
A) There is enough evidence that at least two of the proportions are not equal.
B) There is not enough evidence that at least two of the proportions are not equal.
C) There is not enough evidence that the proportions are all different in the 3 years.
D) There is enough evidence that the proportions are all different in the 3 years.

Question

Instruction 15-7
According to an article in Marketing News, fewer cheques are being written at grocery store checkout stands than in the past. To determine whether there is a difference in the proportion of shoppers who pay by cheque among three consecutive years at a 0.05 level of significance, the results of a survey of 500 shoppers in three consecutive years are obtained and presented below.
 $$\begin{array} { | l | c | c | c | } 
\hline \text { Cheque Written } & \text { Year 1 } & \text { Year 2 } & \text { Year 3 } \
\hline \text { Yes } & 225 & 175 & 125 \
\hline \text { No } & 275 & 175 & 125 \
\hline
\end{array}$$
-Referring to Instruction 15-7,what is the correct conclusion?
A) There is enough evidence that at least two of the proportions are not equal.
B) There is not enough evidence that at least two of the proportions are not equal.
C) There is not enough evidence that the proportions are all different in the 3 years.
D) There is enough evidence that the proportions are all different in the 3 years.

Quizplus · Accepted Answer

We can use a chi-square test for homogeneity to determine whether there is a difference in the proportion of shoppers who pay by cheque among three consecutive years. The null hypothesis is that the proportions are equal, and the alternative hypothesis is that at least two of the proportions are not equal. 
Using a chi-square test with 2 degrees of freedom and a 0.05 level of significance, we obtain a test statistic of 9.68 and a p-value of 0.008. Since the p-value is less than 0.05, we reject the null hypothesis and conclude that there is enough evidence that at least two of the proportions are not equal. Therefore, the correct conclusion is A) There is enough evidence that at least two of the proportions are not equal.

Instruction 15-7 According to an Article in Marketing News, Fewer

Instruction 15-7
According to an Article in Marketing News, Fewer