CONFIDENCE INTERVALS IN HEALTHCARE ADMINISTRATION

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Walden University *

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8800

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Health Science

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Jan 9, 2024

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docx

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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. Testing the systolic blood pressure of a hypothetical population of 100 people. HO: H = 80, H1: 1780 Test Results: 100- piece sample 85 sample mean SD 5 Sample Two sided test run to determine the t test statistic.

X= T= s/n 10.0000 Relevant p-value is 0.0000 for alpha = 0.05 Disregard null hypothesis CI to be calculated 95% t value: 1.9842 Standard error: 0.5000 T c*SE MOE = 0.9921 Lower CI (mean – MOE) = 84.0079 Mean + MOE Upper CI = 85.9921 Range confidence = (84.0079, 85.9921) Since the mean doesn’t fall inside the confidence range, the null hypothesis is rejected. Reference Albright, S. C., & Winston, W. L. (2020). Business analytics: Data analysis and decision making . Cengage Learning, Inc..

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