9231/41/M/J/25q5

Two jigsaw puzzles have the same number of pieces with identical shapes but have different pictures printed on them. One puzzle has a seaside picture and the other has a cartoon picture. A researcher believes that children will complete the cartoon puzzle more quickly. To test this belief, 10 children are randomly selected. The time taken in seconds for each child to complete each puzzle is recorded below.

Child	A	B	C	D	E	F	G	H	I	J
Seaside	182	130	193	181	192	204	184	192	180	189
Cartoon	161	111	195	159	202	200	168	165	145	160

(a) Carry out a Wilcoxon matched-pairs signed-rank test at the 5% significance level to test the researcher’s belief. [6 marks]

(b) Show that using a paired-sample sign test at the 5% significance level would result in the opposite conclusion to that found in part (a). [3 marks]

It was later discovered that the experiment had been conducted such that each child completed the seaside puzzle first followed by the cartoon puzzle.

(c) Comment on the validity of using this experiment to test the researcher’s belief. [1 mark]

Mark Scheme

9231/43/M/J/25q4

A researcher claims that older people take longer to react to a sudden loud noise than younger people. To investigate this, the researcher randomly selects 6 people over 50 years old and 8 people under 25 years old and records their reaction times, in milliseconds, to a sudden loud noise. The reaction times are as follows.

Over 50: 198 212 217 229 235 242

Under 25: 178 181 183 192 203 209 223 231

Carry out a Wilcoxon rank-sum test at the 5% significance level to test the researcher’s claims. [8 marks]

Mark Scheme