Question

In: Statistics and Probability

For each of 12 organizations, the cost of operation per client was found. The 12 scores...

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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Expert Solution

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 .


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