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Use the Z-table in the formula sheet to answer the following question: The waiting time for patients at a polyclinic follows a normal distribution with a mean of 30 minutes and a population standard deviation of 6 minutes

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Use the Z-table in the formula sheet to answer the following question: The waiting time for patients at a polyclinic follows a normal distribution with a mean of 30 minutes and a population standard deviation of 6 minutes. After taking some measures to shorten the patients' waiting time, the quality-assurance department sampled 49 patients and found that the mean waiting time is 27 minutes. What is the probability that the sampled mean waiting time is less than 27 minutes? Is this a likely result? What can you conclude from the result? (a) (5 marks) Using the 95% confidence interval, what is the interval estimate for the mean waiting time? Based on the interval estimate, are the measures effective in reducing patients' waiting time? (b) (4 marks) (c) At the 0.5 significance level, use hypothesis testing method to decide if the sample data support the claim that the measures are effective. Clearly state the steps of hypothesis testing. (6 marks)