Take the question:
A teacher wants to see the effect of changing how reading is taught to primary school children. The children in Year $4$ take a reading test at the end of the year. In previous years the score has had a mean of $60$ and a variance of $400$ and was normally distributed. After the change in teaching method $30$ children took the test and the sample mean was $x̄ = 66$ with a sample variance $s = 225$. The teacher wants to know if changing the teaching method has affected the score on the test. Use a 5% significance level.
Test the hypothesis that the mean is $μ = 60$ against a two-sided alternative.
Now, I'm confused because the answer involves using the test statistics where you don't know the variance but I thought the variance was given in the question as $400$.
I have already answered this question 'Test the null hypothesis that the variance is $σ^2 = 400$ against a two-sided alternative' where I didn't find enough evidence to reject the null hypothesis, maybe this has something to do with my confusion.
Thanks
Edit: Does anyone have any tips?