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):

57 55.9 53.5 66 59.0 64.7 70.1 64.7 53.5 78.2

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.)

x = %
s = %

(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.)

lower limit     %
upper limit     %

Explanation / Answer

a.

Mean(x)=62.26
Standard deviation( sd )=7.9838

b.

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

Sample Size(n)=10
Confidence Interval = [ 62.26 ± t a/2 ( 7.9838/ Sqrt ( 10) ) ]
= [ 62.26 - 1.833 * (2.525) , 62.26 + 1.833 * (2.525) ]
= [ 57.632,66.888 ]

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