3 Past experience has shown that the heights of a certain variety of rose bush have been normally distributed with mean 85.0 cm . A new fertiliser is used and it is hoped that this will increase the heights. In order to test whether this is the case, a botanist records the heights, \(x \mathrm {~cm}\), of a large random sample of \(n\) rose bushes and calculates that \(\bar { x } = 85.7\) and \(s = 4.8\), where \(\bar { x }\) is the sample mean and \(s ^ { 2 }\) is an unbiased estimate of the population variance. The botanist then carries out an appropriate hypothesis test.

1. The test statistic, \(z\), has a value of 1.786 correct to 3 decimal places. Calculate the value of \(n\).
2. Using this value of the test statistic, carry out the test at the \(5 \%\) significance level.