4. A psychologist carries out a survey of the perceived body weight of 150 randomly chosen people. He asks them if they think they are underweight, about right or overweight. His results are summarised in the table below.
| \cline { 2 - 4 }
\multicolumn{1}{c|}{} | Underweight | About right | Overweight |
| Male | 20 | 22 | 30 |
| Female | 16 | 28 | 34 |
The psychologist calculates two of the expected frequencies, to 2 decimal places, for a test of independence between perceived body weight and gender. These results are shown in the table below.
| \cline { 2 - 4 }
\multicolumn{1}{c|}{} | Underweight | About right | Overweight |
| Male | 17.28 | | |
| Female | 18.72 | | |
- Complete the table of expected frequencies shown above.
- Test, at the \(10 \%\) level of significance, whether or not perceived body weight is independent of gender. State your hypotheses clearly.
The psychologist now combines the male and female data to test whether or not body weight types are chosen equally.
- Find the smallest significance level, from the tables in the formula booklet, for which there is evidence of a preference.