What percentage of hospitals provide at least some charity care? Based on a rand

Question

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 of the percentage of hospitals providing at least some charity care. (Round your answers to one decimal place.)

Explanation / Answer

Confidence Interval
CI = x ± t a/2 * (sd/ Sqrt(n))
Where,
x = Mean
sd = Standard Deviation
a = 1 - (Confidence Level/100)
ta/2 = t-table value
CI = Confidence Interval
Mean(x)=62.2
Standard deviation( sd )=8.02
Sample Size(n)=10
Confidence Interval = [ 62.2 ± t a/2 ( 8.02/ Sqrt ( 10) ) ]
= [ 62.2 - 1.833 * (2.5) , 62.2 + 1.833 * (2.5) ]
= [ 57.6,66.8 ]

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