| Date | May 2010 | Marks available | 2 | Reference code | 10M.1.sl.TZ2.9 |
| Level | SL only | Paper | 1 | Time zone | TZ2 |
| Command term | State | Question number | 9 | Adapted from | N/A |
Question
A market researcher consulted males and females to determine whether the type of coffee they drink is associated with gender. The types of coffee are Cappuccino, Latte, Americano, Macchiato and Espresso. A \({\chi ^2}\) test was conducted, at the 5 % significance level and the \({\chi ^2}\) value was found to be 8.73.
Write down the null hypothesis.
Write down the alternative hypothesis.
Write down the number of degrees of freedom for this test.
Write down the critical value for this test.
State whether the type of coffee drunk is independent of gender. Give a reason for your answer.
Markscheme
Type of coffee drunk is independent of gender. (A1)
Note: Accept is “not associated”. Do not accept “not related”, “not correlated” or “not influenced”.
[1 mark]
Type of coffee drunk is not independent of gender. (A1)(ft) (C2)
Note: If hypotheses are reversed award (A0)(A1)(ft).
[1 mark]
4 (A1) (C1)
[1 mark]
\({\chi ^2}({\text{crit}}) = 9.488\) (A1)(ft) (C1)
Note: Accept 9.49.
[1 mark]
\({\chi ^2}({\text{calc}}) < {\chi ^2}({\text{crit}}),{\text{ }}8.73 < 9.488\) (R1)
Accept the null hypothesis (Accept type of coffee is independent of gender). (A1)(ft) (C2)
Notes: Follow through from their answer to part (c).
Do not award (R0)(A1).
[2 mark]
Examiners report
Many candidates gained full marks on this question. However, a number of candidates did not answer at all or stopped after either correctly or incorrectly defining H0 and/or H1. Many incorrect versions of ‘independent’ were seen and candidates should be advised that the terms not related, not correlated and not influenced will not be awarded marks. There were an encouraging number of full marks gained on this question.
Many candidates gained full marks on this question. However, a number of candidates did notanswer at all or stopped after either correctly or incorrectly defining H0 and/or H1. Many incorrect versions of ‘independent’ were seen and candidates should be advised that the termsnot related, not correlated and not influenced will not be awarded marks. There were anencouraging number of full marks gained on this question.
Many candidates gained full marks on this question. However, a number of candidates did not answer at all or stopped after either correctly or incorrectly defining H0 and/or H1. Many incorrect versions of ‘independent’ were seen and candidates should be advised that the terms not related, not correlated and not influenced will not be awarded marks. There were an encouraging number of full marks gained on this question.
Many candidates gained full marks on this question. However, a number of candidates did not answer at all or stopped after either correctly or incorrectly defining H0 and/or H1. Many incorrect versions of ‘independent’ were seen and candidates should be advised that the terms not related, not correlated and not influenced will not be awarded marks. There were an encouraging number of full marks gained on this question.
Many candidates gained full marks on this question. However, a number of candidates did not answer at all or stopped after either correctly or incorrectly defining H0 and/or H1. Many incorrect versions of ‘independent’ were seen and candidates should be advised that the terms not related, not correlated and not influenced will not be awarded marks. There were an encouraging number of full marks gained on this question.
