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Social ScienceWhat 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_______________%
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_______________%
Expert Answer
- 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](https://prod-qna-question-images.s3.amazonaws.com/answer/17028233-0f67-4e90-81a6-699354ba6e4c/183a7ec7-442e-4365-985a-e17fe94a9b21/wcc3zm47.png)
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10 x bar n - 62.28 AVERAGE (A1:A10)] 62.3
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](https://prod-qna-question-images.s3.amazonaws.com/answer/17028233-0f67-4e90-81a6-699354ba6e4c/183a7ec7-442e-4365-985a-e17fe94a9b21/899eyre.png)
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S (7.9304) STDEV(A1:A10] 7.9
B.Computing the 90% confidence interval for population mean:
Confidence interval:
The (1-α) % confidence i...
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