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(a)

In year 2021, the length of time patients required to wait at a hospitalâ€™s waiting area is normally distributed with a mean of 16.1 minutes. In order to improve patientsâ€™ experience, the hospital implemented a new registration system that records the time log of patients at each station or department in the hospital. After implementing the system, it is found that the average waiting time of a sample of 301 patients is 14.3 minutes and standard deviation 9.6 minutes. Based on this data, can the hospital conclude that the average waiting time has decreased? Use a significance level of 5%.

(7 marks)

(b)

From previous data, there appears to be no significant difference in the waiting time for getting a blood test and X-ray scan. The customer service manager of the hospital hypothesizes that average time spent waiting for an X-ray scan is longer than getting a blood test. To verify his claim, he conducted a further study on a sample of 80 randomly selected patients waiting for a blood test and 100 randomly selected patients waiting for an X-ray scan. It was found that the average time spent by those waiting for a blood test and X-ray scan are 12.4 minutes and 14.6 minutes, respectively. The corresponding standard deviations are 8.1 minutes for the blood test patients and 8.3 minutes for the X-ray patients. At the 5% significance level, do the data provide sufficient evidence to support the customer service managerâ€™s claim? Assume that the waiting time is normally distributed and population variances are equal.

(10 marks)

(c)

An independent market survey report stated that 83% of patients in the hospital are satisfied with the services offered by the hospital. The hospitalâ€™s customer service department conducted their own survey three months after the report was released and found that out of the 250 randomly sampled patients, 215 are satisfied with the services. Is there significant evidence to suggest that the proportion of patients who are satisfied with the service now is higher than the percentage reported by the market survey report? Use ?=0.05.

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