government minister makes a claim that, "British workers have never had it so good; the mean yearly salary is 28, 000." A sample of 24 incomes is made and given below (each entry is given in units of 1000): 12.8 25.6 29.7 27.7 28.1 39 15.5 16.6 28.3 106 18.9 19.1 21.5 22.2 17.5 15 10.3 30.2 45 12.5 22.9 23.5 28.1 29.7 i) Find the 95% confidence interval for the mean (i.e average) salary. ii) The opposition claim that this data suggests that, on average, British workers earn less than 28, 000 per year. Perform a suitable hypothesis test to investigate this claim. iii) Scandalously, it emerges that the minister inserted their own salary (106, 000) into the data set in order to manipulate the findings. If you remove this entry does this affect the conclusion of the hypothesis test? iv) Suggest a better way of summarising the earnings of 'the average British worker'