In: Statistics and Probability
For each of 12 organizations, the cost of operation per client was found. The 12 scores have a mean of $2133 and a standard deviation of $345. Assume the population of cost of operation per client follows a normal model. Compute and interpret a 90% CI for the mean cost of operation for all such organizations
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Solution :
Given that,
Point estimate = sample mean = = $ 2133
sample standard deviation = s = $ 345
sample size = n = 12
Degrees of freedom = df = n - 1 = 12 - 1 = 11
At 90% confidence level
= 1 - 90%
=1 - 0.90 =0.10
/2
= 0.05
t/2,df
= t0.05,11 = 1.796
Margin of error = E = t/2,df * (s /n)
= 1.796 * (345 / 12)
Margin of error = E = 178.87
The 90% confidence interval estimate of the population mean is,
± E
= $ 2133 ± $ 178.87
= ( $ 1954.13, $ 2311.87 )
We are 90% confident that the true mean of cost of operation per client between $ 1954.13 and $ 2311.87 .