| Date | May 2008 | Marks available | 11 | Reference code | 08M.3sp.hl.TZ2.3 |
| Level | HL only | Paper | Paper 3 Statistics and probability | Time zone | TZ2 |
| Command term | Justify and State | Question number | 3 | Adapted from | N/A |
Question
A teacher wants to determine whether practice sessions improve the ability to memorize digits.
He tests a group of 12 children to discover how many digits of a twelve-digit number could be repeated from memory after hearing them once. He gives them test 1, and following a series of practice sessions, he gives them test 2 one week later. The results are shown in the table below.
(a) State appropriate null and alternative hypotheses.
(b) Test at the 5 % significance level whether or not practice sessions improve ability to memorize digits, justifying your choice of test.
Markscheme
(a) \({{\text{H}}_0}:d = 0;{\text{ }}{{\text{H}}_1}:d > 0\), where d is the difference in the number of digits remembered A1A1
[2 marks]
(b)
A2
Notes: Award A2 for the correct d values.
Award A1 for one error, A0 for two or more errors.
Use the t-test because the variance is not known M1R1
By GDC
t = 2.106… (A2)
EITHER
p-value = 0.0295 (accept any value that rounds to this number) A2
Since 0.0295 < 0.05 there is evidence that practice sessions improve ability to memorize digits R1
OR
The critical value of t is 1.796 A2
Since 2.106... > 1.796 there is evidence that practice sessions improve ability to memorize digits R1
Note: Award M1R1A1A1R1 for testing equality of means (t = –1.46, p-value = 0.08) .
[9 marks]
Total [11 marks]
Examiners report
Although this question was reasonably well done the hypotheses were often not stated precisely and the fact that the two data sets were dependent escaped many candidates.
