A psychologist believes that an employee’s level of satisfaction with their job changes as the employee gets promoted. Eighteen employees from UK retail companies were randomly selected. A year before each employee received a promotion, a job satisfaction score was recorded. Then a year after the employee was promoted, the job satisfaction score was recorded again. The psychologist wants to investigate the patterns of change in job satisfaction of employees of UK retail companies. Table 2 gives the job satisfaction score before and after promotion, along with the differences between the scores after and before promotion.

Table 2

Employee Job satisfaction score Job satisfaction score Score difference number before promotion after promotion (after–before)

1 87 85 −2 2 84 87 3 3 102 89 −13 4 82 89 7 5 85 85 0 6 85 92 7 7 87 94 7 8 103 88 −15 9 84 84 0 10 87 93 6 11 77 91 14 12 87 88 1 13 77 91 14 14 81 88 7 15 88 88 0 16 87 85 −2 17 102 89 −13 18 95 88 −7

A sign test is to be performed to investigate whether in general the job satisfaction score after promotion differs from the job satisfaction score before promotion.

(a) Write down the hypothesis to be tested. [2] (b) Record the number of values lying above and the number lying below the hypothesised value. What is the value of the test statistic? [2] (c) What is the appropriate critical value at the 5% significance level? [2] (d) Explain whether or not you would reject the hypothesis at the 5% significance level. Justify your answer. [1] (e) Using Figure 9 of Unit 6 (Subsection 4.1), calculate the p-value given by the hypothesis test. [2] (f) Looking at this p-value, and using Table 10 of Unit 6 (Subsection 5.1), what conclusion can be drawn from the hypothesis test? [1] (g) How does this conclusion sit with the result of part (d)? [1] (h) What is your overall conclusion in terms of the difference in job satisfaction after and before promotion, based on these data? [1]