Practise forming hypotheses, choosing significance levels, applying p-values or critical results and interpreting chi-square or t-test conclusions with assumptions.
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.
Use an appropriate test, at the 5 % significance level, to determine whether a new employee staying with the firm is independent of their interview rating. State the null and alternative hypotheses, the p-value and the conclusion of the test.
The next year's group of applicants are asked to complete a written assessment which is then analysed. From those recruited as new employees, a random sample of size 18 is selected.
The sample is stratified by department. Of the 91 new employees recruited that year, 55 were placed in the national department and 36 in the international department.
The written assessment is in five sections, numbered 1 to 5. At the end of the year, the employees are also given a score for each of five professional attributes: V, W, X, Y and Z .
The firm decides to test the hypothesis that there is a correlation between the mark in a section and the score for an attribute.
They compare marks in each of the sections with scores for each of the attributes.
Write down the number of tests they carry out.
The firm obtains a significant result when comparing section 2 of the written assessment and attribute X. Interpret this result.