2 A town council wanted residents to apply for grants that were available for home insulation. In a trial, a random sample of 200 residents was encouraged, either in a letter or by a phone call, to apply for the grants. The outcomes are shown in the table.
| Applied for grant | Did not apply for grant | Total |
| Letter | 30 | 130 | 160 |
| Phone call | 14 | 26 | 40 |
| Total | 44 | 156 | 200 |
- The council believed that a phone call was more effective than a letter in encouraging people to apply for a grant. Use a \(\chi ^ { 2 }\)-test to investigate this belief at the \(5 \%\) significance level.
- After the trial, all the residents in the town were encouraged, either in a letter or by a phone call, to apply for the grants. It was found that there was no association between the method of encouragement and the outcome. State, with a reason, whether a Type I error, a Type II error or neither occurred in carrying out the test in part (a).
(2 marks)