What percentage of hospitals provide at least some charity care? Based on a random sample of hospital reports of eastern states, the following information is obtained (units in percentage of hospitals providing at least some charity care):57.4   56.4  53.2  65.6  59.0  64.7  70.1   64.7  53.5  78.2Assume that the population x values an approximetely normal distribution.a) Use a calculater with mean and sample deviation keys to find the sample mean percentage x bar and sample standard deviation s. ( Round answers to one decimal place)A)     x bar=  _____________%        s      =_______________%B)     Find a 90% Confidence Interval for the population average Mu of the percentage of hospitals providing at least some charity care. (Round to one decimal place.)Lower Limit_______________%Upper Limit_______________%

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Asked Jul 1, 2019
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What percentage of hospitals provide at least some charity care? Based on a random sample of hospital reports of eastern states, the following information is obtained (units in percentage of hospitals providing at least some charity care):

57.4   56.4  53.2  65.6  59.0  64.7  70.1   64.7  53.5  78.2

Assume that the population x values an approximetely normal distribution.

a) Use a calculater with mean and sample deviation keys to find the sample mean percentage x bar and sample standard deviation s. ( Round answers to one decimal place)

A)     x bar=  _____________%

        s      =_______________%

B)     Find a 90% Confidence Interval for the population average Mu of the percentage of hospitals providing at least some charity care. (Round to one decimal place.)

Lower Limit_______________%

Upper Limit_______________%

 

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Step 1
  1. Finding the mean and standard deviation of the variable X.

Mean:

The general formula to obtain the mean of a random variable is,

Mean = (Sum of X values)/n.

In columns of A1:A10 in Excel, enter the sample data.

In column B1, enter the Excel function “=AVERAGE(A1:A10)”.

The mean of the variable X is obtained as 62.3 % from the calculations given below:

10
x bar
n
- 62.28
AVERAGE (A1:A10)]
62.3
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10 x bar n - 62.28 AVERAGE (A1:A10)] 62.3

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Step 2

Standard deviation:

The general formula to obtain the standard deviation of a random variable is,

s = sqrt (sum of values of X2  /n – (mean)2 ).

In column B2, enter the Excel function “=STDEV(A1:A10)”.

The standard deviation of a random variable X is obtained as 7.9 % from the calculations given below:

S (7.9304) STDEV(A1:A10]
7.9
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S (7.9304) STDEV(A1:A10] 7.9

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Step 3

B.Computing the 90% confidence interval for population mean:

Confidence interval:

The (1-α) % confidence i...

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