North York General Hospital, a multi-site community teaching hospital, gets approxi- mately 75,000 visits to its emergency department each year. With that many patients, Emergency was often very overcrowded and patients weren't flowing through care as they should. North York General Hospital used "Lean Tools," a quality improvement method that emphasizes reducing waste in the work environment in its many forms to create a productive work environment and a journey through the system for the patient that is as smooth and efficient as possible. Between November 2006 and September 2008, North York General Hospital achieved a reduction in the average time to see a physician. More specifically, the average time to see a physician in sub-acute care decreased from 3.3 hours to 2.8 hours. Suppose a sample of 100 waiting times before 2006, and between 2006 and September 2008 were randomly selected from the hos- pital records for each of the two time periods. The sample statistics are listed below:

a. Give a point estimate for the true mean waiting time after the quality improve- ment and the margin of error.

b. Construct a 90% confidence interval for the true mean waiting time after quality improvement. Interpret your confidence interval.

c. Based on the interval in part

b, can the hospital's claim be rejected? Justify your answer.

d. Suppose that the quality control department of this hospital intends to have the wait- ing time of 2.7 hours on average to see a physician in sub-acute care. Should the confidence interval in part b concern the quality control department? Explain.

e. If the distribution of the waiting time is not normal, you can still use the standard normal distribution to construct a confidence interval for 2. Why?

f. Now, suppose for a future survey the hospital administrator wishes to estimate 2. How many records should be sampled in order to estimate ? The administrator would like the margin of error to be less than 0.5 hours with a confidence of 0.95, using standard deviation of 1.7. g. Let u be the true mean waiting time before the quality improvement. What is the best point estimator for (u), the difference in average waiting time before and after the quality improvement? h. Describe completely the sampling distribution of the point estimator for (-2) and calculate the margin of error. i. Find a 98% confidence interval for ( - 12). j. Based on the interval in part i, can one conclude there is a difference in the true average waiting time before quality improvement and after? Justify your answer. k. What does the phrase "98% confident" mean?

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Waiting Time Before Quality Improvement Sample Statistic Sample size 100 Sample mean 3.5 Sample variance 2.82 Waiting Time After Quality Improvement 100 3.1 1.68