Question

# What percentage of hospitals provide at least some charity care? Based on a random sample of...

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):

 57.2 55.7 52.9 65.7 59 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 μ of the percentage of hospitals providing at least some charity care. (Round your answers to one decimal place.)

 lower limit % upper limit %

a)

Sample Mean,    x̅ = ΣX/n =    62.2%

sample std dev ,    s = √(Σ(X- x̅ )²/(n-1) ) =   8.0 %

b)

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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