A machine is designed to fill each container with 300 ml of fruit juice. It may be assumed that the volume of fruit juices in a container follows a normal distribution. A random sample of 12 containers has a sample mean of 291 ml and a sample standard deviation of 8 ml. Let denote the mean volume of fruit juice in a container that is filled by the machine. (a) Carry out a two-tailed test of the null hypothesis Ho : μ = 300 versus the alternative H₁:300 with the level of significance a = 5%. Consider the following Confidence Intervals: Confidence Interval A: (294.9, 305.1) Confidence Interval B: (285.9, 296.1) Confidence Interval C: (295.5, 304.5) Which of the above Confidence Intervals, if any, is the 95% confidence interval that can be used for the test? Enter A, B or C in the answer box for Confidence Intervals A, B or C respectively. If none of them is the correct Confidence Interval, enter N in the answer box. Answer: N (b) What is the conclusion of the test? In the answer box, enter R for 'reject Ho' and DNR for 'do not reject Ho'. If the test is inconclusive, enter N. Answer: R (c) What is the p-value of the test? Give your answer to 3 decimal places in the answer box. Answer: 0.002

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