Black Americans account for 22% of yearly cases of Multiple Myeloma (Awidi and Al Hadidi, 2021). Suppose we are analyzing data from a clinical trial of Multiple Myeloma where patients were enrolled from specific clinical centers. It is found that 4.5% of the 800 patients on the trial self-identify as Black. That is, 36 out of 800 patients are Black.

Create a 95% confidence interval for the true proportion of patients who are Black Americans among the clinical centers participating in this clinical trial.

b. Based on the confidence interval you constructed, does there appear to be evidence that the true proportion of Black Americans among these clinical centers is the same as the national proportion of 22%, at the 0.05 level.