Interpret an upper-tail p-value in context

Based on past data, the mean number of dengue cases per day was reported as 30. The authorities suspect that the recent hot and wet weather has increased the mean number of dengue cases per day. A random sample of 60 days is taken and the number of dengue cases per day, $X$, is summarised by

$\sum(x-8)=1400,\qquad\sum(x-8)^2=34800.$

(i) Calculate unbiased estimates of the mean and variance of $X$.2 marks

(ii) Test, at the 5% significance level, whether the mean number of dengue cases per day has increased.4 marks

Explain, in the context of the question, the meaning of the p-value.1 mark