A laboratory in New York is interested in finding the mean chloride level for a healthy resident in the state. A random sample of 50 healthy residents has a mean chloride level of 105 mEq/L. If it is known that the chloride levels in healthy individuals residing in New York have a standard deviation of 37 mEq/L, find a 95% confidence interval for the true mean chloride level of all healthy New York residents. Then complete the table below. What is the lower limit of the 95% confidence interval? What is the upper limit of the 95% confidence interval?
Given n = sample size = 50
xbar = sample mean = 105
= population standard deviation = 37
The 95% confidence interval forthe true mean chloride level of all healthy New York residents
xbar - Za/2*(/√n) < < xbar + Za/2*(/√n)
For a = 0.05 , Za/2 = Z0.025 = 1.96
105 - 1.96*(37/√50) < < 105 + 1.96*(37/√50)
94.74 < < 115.26
Lower limit = 94.74
Upper limit = 115.26
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