Past experience has shown that the heights of a certain variety of rose bush have been normally distributed with mean $85.0{\text{ }}cm$. 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, $x{\text{ }}cm$, of a large random sample of $n$ rose bushes and calculates that $\overline x  = 85.7$ and $s = 4.8$, where $\overline 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.

a) The test statistic, $z$, has a value of $1.786$ correct to 3 decimal places. Calculate the value of $n$.

b) Using this value of the test statistic, carry out the test at the 5% significance level.