4.12 Data collection, reliability and validityIB Maths: Applications and Interpretation HL: Mind map

Exam questions on 4.12 Data collection, reliability and validity

1. A school council wants to find out how students feel about the new canteen menu. One member suggests asking students as they leave the canteen at lunchtime: "Don't you agree that the new menu is far healthier and tastier than the old boring one?"
   Explain why asking only students who are leaving the canteen at lunchtime may give biased results.2 marks
2. A psychologist designs a 20-question questionnaire to measure exam anxiety. She gives it to 40 students and then gives it to the same students again two weeks later. The Pearson's product-moment correlation coefficient between the two sets of scores is $r=0.91$. She also compares the scores with a diagnosis of exam anxiety made independently by a school counsellor.
   Explain what is meant by validity, and state the type of validity test carried out when the scores are compared with the counsellor's diagnosis.2 marks
3. A researcher records, for 155 students, the number of hours slept the previous night and whether the student felt alert in the first lesson. The numbers of students who felt alert and who did not feel alert were: under 5 hours: 1 and 5; 5 to under 6 hours: 9 and 15; 6 to under 7 hours: 25 and 25; 7 to under 8 hours: 32 and 15; 8 hours or more: 20 and 8. In total 87 students felt alert. A $\chi^2$ test for independence is to be carried out.
   Show that the expected number of students who slept under 5 hours and felt alert is $3.37$ to 3 significant figures, and explain which categories should be combined, giving a reason.3 marks