Waiting times in the emergency room effect patient satisfaction, quality of care, and costs to the facility. Patient waiting time is measured from time of registration to time of discharge. A variable that affects this wait time is if the patient receives diagnostic testing by radiology exams which take more time to get results. The hypothesis is that the average patient in the ED is waiting no more than three hours and the variable is patients requiring radiology testing. The null and alternative hypotheses are expressed in terms of a population proportion, mean, or difference between two means (Banerjee, Jadhav, & Bahwalkar, 2009). A hypothesis is a claim about a population or some other characteristic about a population (Bennett, Briggs, & Triola, 2018). 85 patients are seen in the emergency department that require CTs, MRIs and other radiology testing. 50 waited 3 hours, or 180 minutes. 10 waited 2.5 hours, and 25 waited 3.5 hours to be seen, tested, and discharged home. The hypothesis mean is 180 minutes, the sample mean is 177.6 minutes, the standard deviation is 180, with a standard score of -0.1229. The Null hypothesis is = 180 minutes and the alternative or complement hypothesis is < 180 minutes. Due to patients receiving more tests, there are more patients with a longer than expected wait time giving us a a right tailed hypothesis test with 75 patients waiting equal to or greater than 3 hours. The population parameter is greater than the claimed value. Since the standard score of -0.1229 is less than 1.645 we do not reject the null hypothesis. Since we are not rejecting the null hypothesis, we will reject the alternative hypothesis.
Banerjee, A., Jadhav, S. L., & Bahwalkar, J. (2009). Probability, Clinical Decision Making, and Hypothesis Testing. Industrial Psychiatry Journal, 64-69.
Bennett, J., Briggs, W., & Triola, M. (2018). Statistical Reasoning for Everyday Life (5th ed.). Boston: Pearson.