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# Statistics: Working with Random Samples of Patients

You work at a major regional hospital and you are concerned about waiting times in the emergency room. This file contains data on some random samples of patients. Use the data to answer the following questions.

Problem 1: Column A contains wait times (in minutes) from arrival to triage from a sample of 100 patients. Your emergency room sees 80,000 patients per year. Hospital administrators have claimed that the average arrival-triage wait time is ten minutes.
a) Construct a 95% confidence interval for the population mean arrival-triage wait time.
b) Construct a 95% confidence interval for the total time spent waiting for triage throughout the year.
c) Based on your answer in part (a) (and part (b) if you did that), explain (in plain English) what these results mean.

Excel Tips: The Excel functions =TDIST and =TINV are similar to the functions =NORMSDIST and =NORMSINV and can be used to calculate T critical values. See the Excel helpfile for instructions on the syntax for this function.

Problem 2: A major concern with long ER wait times is that patients may leave the ER without being seen, due to dissatisfaction with having to wait. Other hospitals in the region have patients leave the ER without being seen at a rate of 5%. You are interested to see if your rate is the same as those hospitals nearby. You collect a random sample of 1000 ER visitors. Of those 1000 visitors, 28 left without receiving any treatment. Construct a 95% confidence interval for the population proportion of ER patients that leave without receiving any treatment. Interpret your findings with respect to the 5% figure in other area hospitals.

Problem 3: When discussing wait times, there are typically four figures of interest: arrival to triage (discussed in problem 1), triage to ER, wait to see a provider once in the ER, and overall arrival to provider wait times. The hospital would like to ensure that the overall arrival to provider wait time is less than 60 minutes. Column B has overall wait times for a random sample of 150 patients.
a) Using alpha=0.05, conduct a one-tailed t test of the hypothesis that average wait time is less than 60 minutes. Use m <= 60 as your null hypothesis
b) What is the p value associated with your sample mean weight?
c) What conclusions can you draw from these results?

Excel Tips: By default, =TINV assumes a 2-tailed t test. If you want to calculate a p-value using a 1-tailed t test, simply double the probability you enter into the formula. =TDIST is not capable of dealing with negative numbers. If your t test statistic is negative, use =ABS to make it positive so =TDIST can work correctly.

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