Question 3 10 marks A researcher is interested in whether the population mean mass values are the same for mass 1 and mass 2 for all GWTC runs. (a) Using the file GW Data.mwx, complete Table 2 below and include it in your answer. You should round your answers to a suitable level of accuracy. Table 2 Batch size, mean and standard deviation for the M1 source and M2 source mass values Statistic Batch size M1 source M2 source Mean Standard deviation (b) Using your answers to part (a), do the mean numbers of source mass values and the spread of values seem similar for the M1 source and M2 source masses? Justify your opinions. (c) Without using Minitab, carry out a two-sample z-test of the null hypothesis that the population mean mass values are the same for M1 source and M2 source masses and the alternative hypothesis that the population mean mass values are not the same. Use notation, which you should define. Show your working at each stage and make sure that you explicitly state: the hypotheses being tested the calculation and value of the estimated standard error the calculation and value of the test statistic a comparison of the test statistic against the appropriate values for CV5 and CV1 the conclusions from your test. (d) Why is it appropriate to use the two-sample z-test in this case, rather than the two-sample t-test? [2] [1] [6] [1]