What percentage of hospitals provide at least some charity care? Based on a random sample of 10 hospital reports from eastern states, the sample mean was x = 62.3 % and the sample standard deviation was s = 8.0 %. a. Find a 98% confidence interval for the population average µ of the percentage of hospitals providing at least some charity care. b. Interpretation. What does the confidence interval mean in the context of this problem
What percentage of hospitals provide at least some charity care? Based on a random sample of 10 hospital reports from eastern states, the sample mean was x = 62.3 % and the sample standard deviation was s = 8.0 %. a. Find a 98% confidence interval for the population average µ of the percentage of hospitals providing at least some charity care. b. Interpretation. What does the confidence interval mean in the context of this problem?
Solution:
a.
Let X be the percentage of hospitals provide at least some charity care.
From the given information, x-bar is 62.3%, S=8% and n=10.
The confidence level is 0.98.
Then, the 98% confidence interval for the population average of the percentage of hospitals providing at least some charity care is
Thus, the 98% confidence interval for the population average of the percentage of hospitals providing at least some charity care is between 55.2% and 69.4%.
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