Hypothesis testing — practice question

One-year-old trees of a particular variety are understood to have a mean height of $2.3\,\text{m}$. A scientist thinks that, on average, trees of this age and variety in her area are a little taller than those elsewhere. She intends to perform a hypothesis test at the $2\%$ significance level to check her idea. She chooses a random sample of 100 such trees in her area and records their heights, $h\,\text{m}$. Her data are shown below: $n=100, \quad \sum h=238, \quad \sum h^2=580$.