3 In this question you must show detailed reasoning.
A student is investigating what people think about organic food. She wishes to see if there is any difference between the opinions of females and males. She takes a random sample of 100 people and asks each of them if they think that organic food is better for their health than non-organic food. She will use the data to conduct a hypothesis test. The table below shows the opinions of these 100 people.
| \cline { 3 - 4 }
\multicolumn{2}{c|}{} | Sex | |
| \cline { 3 - 4 }
\multicolumn{2}{c|}{} | Female | Male |
| \multirow{2}{*}{} | Organic better | 35 | 18 |
| \cline { 2 - 4 } | Not better | 22 | 25 |
- Explain why the student should use a random sample.
- Carry out a test at the \(5 \%\) significance level to examine whether there is any association between a person's sex and their opinion on organic food. Show your calculations.