Responses to a survey question about color preference for a candy are broken down according to gender in the table given below. At the 0.05 significance level, test the claim that candy color preference and gender are independent.
$\begin{array} { l | l l l }
& \text { Red } & \text { Blue } & \text { Yellow } \
\hline \text { Male } & 25 & 50 & 15 \
\text { Female } & 20 & 30 & 10
\end{array}$
What is your conclusion about the null hypothesis and about the claim?
A) Fail to reject the null hypothesis. There is not sufficient evidence to warrant rejection of
The claim that candy color preference and gender are independent.
B) Reject the null hypothesis. There is not sufficient evidence to warrant rejection of the
Claim that candy color preference and gender are independent.
C) Fail to reject the null hypothesis. There is sufficient evidence to warrant rejection of the
Claim that candy color preference and gender are independent.
D) Reject the null hypothesis. There is sufficient evidence to warrant rejection of the claim
That candy color preference and gender are independent.

Question

Responses to a survey question about color preference for a candy are broken down according to gender in the table given below. At the 0.05 significance level, test the claim that candy color preference and gender are independent. 
$\begin{array} { l | l l l } 
& \text { Red } & \text { Blue } & \text { Yellow } \
\hline \text { Male } & 25 & 50 & 15 \
\text { Female } & 20 & 30 & 10
\end{array}$
What is your conclusion about the null hypothesis and about the claim?
A) Fail to reject the null hypothesis. There is not sufficient evidence to warrant rejection of
The claim that candy color preference and gender are independent.
B) Reject the null hypothesis. There is not sufficient evidence to warrant rejection of the
Claim that candy color preference and gender are independent.
C) Fail to reject the null hypothesis. There is sufficient evidence to warrant rejection of the
Claim that candy color preference and gender are independent.
D) Reject the null hypothesis. There is sufficient evidence to warrant rejection of the claim
That candy color preference and gender are independent.

Quizplus · Accepted Answer

To determine if candy color preference and gender are independent, a chi-square test of independence is used. Without calculating the exact chi-square statistic and comparing it to a critical value (due to the lack of specific calculation details), the conclusion to "fail to reject the null hypothesis" suggests that the observed differences in preferences could be due to chance. Therefore, there isn't sufficient evidence to conclude that candy color preference and gender are dependent, supporting the claim of independence.

Responses to a Survey Question About Color Preference for a Candy