(Solved): Advanced level maths. hypothesis testing. need helps. The marks of students taking a Mathemat ...

Advanced level maths. hypothesis testing. need helps.

The marks of students taking a Mathematics examination were normally distributed with mean $m$. The marks $x$, of 400 randomly chosen students whose scripts were marked by a particular examiner were recorded and are summarised as follows. $?(x?50)=3000?(x?50{)}^2=233571$ Find the unbiased estimates of the population mean and variance. If $m=60$, test at the 5\% significance level whether the examiner was marking too strictly is justified. Hint: Use $s^2$ for the hypothesis test since ${?}^2$ is unknown.