Find significance levels that reject a wage claim

In year 2008, a survey was done by the Ministry of Manpower (MOM) to determine the amount of daily wages, denoted as $X$, that part-time workers were receiving. Past records show that on average, the wages that each worker received was $30.

A year later, MOM wants to find out if there is a change in the mean wage. Data from 90 workers are collected and their wages are summarized as shown below:

$\bar x=31,\qquad\sum(x-31)^2=1947.$

Calculate the unbiased estimate of the variance of $X$.1 mark

MOM decides to do a test on the collected data. Find the range of values of $\alpha$ if MOM were to conclude that there is a change in the mean wage at $\alpha\%$ level of significance.3 marks