Yates' correctionAQA A-Level Further Maths: Subtopic test

1. 1
   A gardener compares germination for 60 seeds given fertiliser and 60 seeds given none. Of the seeds given fertiliser, 42 germinate. Of the seeds given none, 30 germinate. A chi-squared test for association between treatment and germination is to be carried out.

   (a)

   Assuming no association, find the expected number of seeds given fertiliser that germinate.

   [1 mark]

   • A$42$
   • B$30$
   • C$24$
   • D$36$

   (b)

   Which expression gives Yates' corrected test statistic?

   [1 mark]

   • A$\sum\frac{(|O-E|-0.5)^2}{E}$
   • B$\sum\frac{(|O-E|+0.5)^2}{E}$
   • C$\sum\frac{(O-E-0.5)^2}{E}$
   • D$\sum\frac{(|O-E|-0.5)^2}{O}$

   (c)

   State the degrees of freedom of the test statistic and explain why Yates' correction is applied.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A survey of 50 people records which of two products, A or B, each prefers. Of the 30 men, 20 prefer A and 10 prefer B. Of the 20 women, 6 prefer A and 14 prefer B.

   (a)

   Assuming preference is independent of sex, find the expected number of men who prefer B.

   [1 mark]

   • A$15.6$
   • B$14.4$
   • C$10.4$
   • D$12.0$

   (b)

   Using Yates' correction, find the contribution to the test statistic from the men who prefer A.

   [1 mark]

   • A$1.24$
   • B$1.54$
   • C$0.975$
   • D$0.282$

   (c)

   Calculate the value of the test statistic with Yates' correction applied.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A trial compares two treatments for a skin condition. Of 20 patients given treatment A, 14 were cured. Of 20 patients given treatment B, 8 were cured.

   (a)

   Calculate the value of the test statistic with Yates' correction applied.

   [3 marks]

   (b)

   Using the corrected test statistic $2.53$, test at the $5\%$ significance level whether the cure rate is associated with the treatment.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A company trials two training methods, X and Y. Of 25 employees trained by method X, 17 pass the assessment. Of 25 employees trained by method Y, 10 pass the assessment.

   (a)

   Carry out a chi-squared test, at the $5\%$ significance level and using Yates' correction, to investigate whether the pass rate is associated with the training method.

   [6 marks]

   (b)

   A colleague omits Yates' correction. Evaluate how this changes the test in part (a) and which statistic should be used.

   [6 marks]

   Total for question 4: 12 marks

End of questions