IB Maths AI HL 4.18 Advanced hypothesis testing Question Bank

A firm wishes to review its recruitment processes. This question considers the validity and reliability of the methods used.
Every year an accountancy firm recruits new employees for a trial period of one year from a large group of applicants.
At the start, all applicants are interviewed and given a rating. Those with a rating of either Excellent, Very good or Good are recruited for the trial period. At the end of this period, some of the new employees will stay with the firm.
It is decided to test how valid the interview rating is as a way of predicting which of the new employees will stay with the firm.
Data is collected and recorded in a contingency table.

For the data in this table, test the null hypothesis, $\mathrm{H}_{0}: \rho=0$, against the alternative hypothesis, $\mathrm{H}_{1}: \rho>0$, at the 5 % significance level. You may assume that all the requirements for carrying out the test have been met.