Discussion: Confidence Intervals in Healthcare Administration
Healthcare administration leaders are asked to make evidence-based decisions on a daily basis. Sometimes, these decisions involve high levels of uncertainty, as you have examined previously. Other times, there are data upon which evidence-based analysis might be conducted.
This week, you will be asked to think of scenarios where building and interpreting confidence intervals (CIs) would be useful for healthcare administration leaders to conduct a two-sided hypothesis test using fictitious data.
For example, Ralph is a healthcare administration leader who is interested in evaluating whether the mean patient satisfaction scores for his hospital are significantly different from 87 at the .05 level. He gathers a sample of 100 observations and finds that the sample mean is 83 and the standard deviation is 5. Using a t-distribution, he generates a two-sided confidence interval (CI) of 83 +/- 1.984217 *5/sqrt(100). The 95% CI is then (82.007, 83.992). If repeated intervals were conducted identically, 95% should contain the population mean. The two-sided hypothesis test can be formulated and tested just with this interval. Ho: Mu = 87, Ha: Mu<>87. Alpha = .05. If he assumes normality and that population standard deviation is unknown, he selects the t-distribution. After constructing a 95% CI, he notes that 87 is not in the interval, so he can reject the null hypothesis that the mean satisfaction rates are 87. In fact, he has an evidence-based analysis to suggest that the mean satisfaction rates are not equal to (less than) 87.
For this Discussion, review the resources for this week, and consider how a CI might be used to support hypothesis testing in a healthcare scenario.
By Day 3
Post a description of a healthcare scenario where a CI might be used, and then complete a fictitious two-sided hypothesis test using a CI and fictitious data.
Albright, S. C., & Winston, W. L. (2017). Business analytics: Data analysis and decision making (6th ed.). Stamford, CT: Cengage Learning. Chapter 8, “Confidence Interval Estimation”Chapter 9, “Hypothesis Testing”