4 The height \(H\), in metres, of mature trees of a certain variety is normally distributed with standard deviation 0.67. In order to test whether the population mean of \(H\) is greater than 4.23, the heights of a random sample of 200 trees are measured.

1. Write down suitable null and alternative hypotheses for the test.
   The sample mean height, \(\bar { h }\) metres, of the 200 trees is found and the test is carried out. The result of the test is to reject the null hypothesis at the 5\% significance level.
2. Find the set of possible values of \(\bar { h }\).
3. Ajit said, 'In (b) we had to assume that \(\bar { H }\) is normally distributed, so it was necessary to use the Central Limit Theorem.' Explain whether you agree with Ajit.