A food processing plant packs cereal into boxes with a target mean weight of 500g. A quality control inspector believes the machine is underfilling the boxes. A random sample of 100 boxes is weighed, giving the following statistics:
n=100∑x=49910∑x2=24912581 n = 100 \quad \sum x = 49910 \quad \sum x^2 = 24912581 n=100∑x=49910∑x2=24912581Find the mean and standard deviation of the sample.
Carry out a hypothesis test to test the inspector's belief at the 1% significance level. State your assumptions clearly.
