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.
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.
Expert Solution Preview
Introduction:
As a medical professor, it is important to encourage students to think critically and apply statistical concepts in healthcare scenarios. This week’s task involves identifying scenarios where confidence intervals (CIs) can be used to support hypothesis testing in healthcare. In this answer, we will provide an example of how a CI can be used in a healthcare scenario and conduct a two-sided hypothesis test using fictitious data.
Answer:
A healthcare scenario where a CI might be used is in evaluating the efficacy of a new drug for treating hypertension. Suppose a pharmaceutical company conducts a clinical trial to determine whether its new drug is effective in lowering blood pressure levels. The trial involves a sample of 200 patients with hypertension, and the company wants to test if the mean reduction in blood pressure levels with the new drug is significantly different from 10 mmHg, with a significance level of 0.05.
Using fictitious data, suppose the sample mean reduction in blood pressure levels with the new drug is 7 mmHg, with a standard deviation of 2 mmHg. To construct a 95% CI for the true mean reduction in blood pressure levels, we can use the formula:
CI = x̄ ± t α/2 * s/√n
where x̄ is the sample mean, s is the sample standard deviation, n is the sample size, and tα/2 is the t-score corresponding to the chosen level of significance and degrees of freedom (df = n – 1).
For a significance level of 0.05 and df = 199, tα/2 = 1.972. Plugging in the values, we get:
CI = 7 ± 1.972 * 2/√200
CI = (6.62, 7.38)
Since the CI does not include the hypothesized value of 10 mmHg, we can reject the null hypothesis that the mean reduction in blood pressure levels is equal to 10 mmHg, and conclude that there is evidence to suggest that the new drug is effective in lowering blood pressure levels.
In conclusion, confidence intervals can be useful in healthcare scenarios where there is a need to test hypotheses about population parameters. By constructing a CI based on sample data, healthcare administrators can make evidence-based decisions that support effective patient care and treatment.
