What percentage of hospitals provide at least some charity care? Based on a random sample of hospital reports from eastern states, the following information is obtained (units in percentage of hospitals providing at least some charity care):
Assume that the population of x values has an approximately normal distribution.
(a) Use a calculator with mean and sample standard deviation keys to find the sample mean percentage x and the sample standard deviation s. (Round your answers to one decimal place.)
(b) Find a 90% confidence interval for the population average μ of the percentage of hospitals providing at least some charity care. (Round your answers to one decimal place.)
Sample Mean, x̅ = ΣX/n = 62.2%
sample std dev , s = √(Σ(X- x̅ )²/(n-1) ) = 8.0 %
degree of freedom= DF=n-1= 9
't value=' tα/2= 1.8331 [Excel formula =t.inv(α/2,df) ]
Standard Error , SE = s/√n = 2.5448
margin of error , E=t*SE = 4.665
confidence interval is
Interval Lower Limit= x̅ - E = 57.5 %
Interval Upper Limit= x̅ + E = 66.8 %
confidence interval is ( 57.5 < µ < 66.8 )
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