3 A company which employs 600 staff wishes to improve its image by introducing new uniforms for the staff to wear. The human resources manager would like to obtain the views of the staff. She decides to do this by means of a systematic sample of \(10 \%\) of the staff.

1. How should she go about obtaining such a sample, ensuring that all members of staff are equally likely to be selected? Explain whether this constitutes a simple random sample. At a later stage in the process, the choice of uniform has been reduced to two possibilities. Twelve members of staff are selected to take part in deciding which of the two uniforms to adopt. Each of the twelve assesses each uniform for comfort, appearance and practicality, giving it a total score out of 10. The scores are as follows.

   Staff member	1	2	3	4	5	6	7	8	9	10	11	12
   Uniform A	4.2	2.6	10.0	9.0	8.2	2.8	5.0	7.4	2.8	6.8	10.0	9.8
   Uniform B	5.0	5.2	1.4	2.8	2.2	6.4	7.4	7.8	6.8	1.2	3.4	7.6

   A Wilcoxon signed rank test is to be used to decide whether there is any evidence of a preference for one of the uniforms.
2. Explain why this test is appropriate in these circumstances and state the hypotheses that should be used.
3. Carry out the test at the \(5 \%\) significance level.