The module team wants to use the data to assess the claim that the population mean percentage of students studying for a Maths degree is 15 percentage points different from the population mean percentage of students studying for a Maths and Stats degree. The team decides to look at the differences in percentages of students studying foraMaths degree and the percentages studying for a Maths and Stats degree. They conduct a one sample z-test on the differences in percentages to test the claim. Write down suitable null and alternative hypotheses to test this claim, stating clearly the meaning of any symbols you use.

They decided to also conduct a sign test that the median difference in the percentage of students studying for a Maths degree and the percentage studying for a Maths and Stats degree is 15 percentage points. It turns out that in the set of differences there are 10 values below 15, 17 values above 15 and one value is exactly 15. Complete the sign test and interpret the results.