- (a) Explain briefly the method of quota sampling.
(b) Give one disadvantage of quota sampling compared with stratified sampling.
(c) Describe a situation in which you would choose to use quota sampling rather than stratified sampling and explain why.
(2 marks) - Commentators on a game of cricket say that a certain batsman is "playing shots all round the ground". A sports statistician wishes to analyse this claim and records the direction of shots played by the batsman during the course of his innings. She divides the \(360 ^ { \circ }\) around the batsman into six sectors, measuring the angle of each shot clockwise from the line between the wickets, and obtains the following results:
| Sector | \(0 ^ { \circ } -\) | \(45 ^ { \circ } -\) | \(90 ^ { \circ } -\) | \(180 ^ { \circ } -\) | \(270 ^ { \circ } -\) | \(315 ^ { \circ } - 360 ^ { \circ }\) |
| No. of Shots | 18 | 19 | 15 | 20 | 9 | 15 |
Stating your hypotheses clearly and using a \(5 \%\) level of significance test whether or not these data can be modelled by a continuous uniform distribution.
(9 marks)