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):

57.4

56.3

53

65.7

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 bar = ? %

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 + ? %

Answer 1

a. %

Create the following table.

data	data-mean	(data - mean)2
57.4	-4.86	23.6196
56.3	-5.96	35.5216
53	-9.26	85.7476
65.7	3.44	11.8336
59.0	-3.26	10.6276
64.7	2.44	5.9536
70.1	7.84	61.4656
64.7	2.44	5.9536
53.5	-8.76	76.7376
78.2	15.94	254.0836

Find the sum of numbers in the last column to get.

So standard deviation is %

b. t value for 9 df is TINV(0.1,9)=1.8

So Margin of Error is

Hence CI is

So lower limit is 57.7%

Upper limit is 66.9%