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Question 3 A machine packages sugar in bags with mean 250g and standard deviation 5g. After a power cut, the standard deviation of the masses of the bags is assumed to be the same. A test at the 5% level of significance is carried out, using a random sample of size 50 with mean 251.9g, to determine whether the mean mass of the bags has changed. A. Explain why a one tailed test is NOT appropriate in this case. (2 marks) B. Using symbols only, formulate appropriate null and alternative hypotheses. (4 marks) C. Identify the distribution of the sample mean under the null hypotheses, stating its mean and variance. (4 marks) D. Calculate the test statistic. (4 marks) E. Determine the critical region for this significance test. (3 marks) F. Supporting your conclusion, state the outcome of the test