4 It is claimed that the area within which a school is situated affects the age profile of the staff employed at that school. In order to investigate this claim, the age profiles of staff employed at two schools with similar academic achievements are compared.
Academia High School, situated in a rural community, employs 120 staff whilst Best Manor Grammar School, situated in an inner-city community, employs 80 staff.
The percentage of staff within each age group, for each school, is given in the table.
| Age | | |
| \(\mathbf { 2 2 - } \mathbf { 3 4 }\) | 17.5 | 40.0 |
| \(\mathbf { 3 5 - } \mathbf { 3 9 }\) | 60.0 | 45.0 |
| \(\mathbf { 4 0 - } \mathbf { 5 9 }\) | 22.5 | 15.0 |
- Form the data into a contingency table suitable for analysis using a \(\chi ^ { 2 }\) distribution.
(2 marks) - Use a \(\chi ^ { 2 }\) test, at the \(1 \%\) level of significance, to determine whether there is an association between the age profile of the staff employed and the area within which the school is situated.
- Interpret your result in part (a)(ii) as it relates to the 22-34 age group.