SOLUTION: Construct the confidence interval for the population mean c= 0.95, x = 15.7, s =10.0, and n=85 A 95% confidence interval for y is (, ). Round to one decimal place as needed.

Question 739753: Construct the confidence interval for the population mean
c= 0.95, x = 15.7, s =10.0, and n=85
A 95% confidence interval for y is (, ). Round to one decimal place as needed.
I am sorry I did not know how to enter the population mean symbol or the line over the x in the problem. Thanks

Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
From your statement of the problem, I assume the following:
x is the sample mean = 15.7
n is the population size = 85
since we do not know the variance, we need to use the t-distribution and the first step is to calculate the standard error,
standard error (SE) = s / sqrt of the population size = 10 / sqrt (85) = 1.08
also the degree of freedom (DF) is 85 - 1 = 84
we now reference the t distribution for a DF of 84 for 95% confidence interval is 1.99
we can now calculate the lower and upper ranges of the 95% confidence interval
Lower Limit = 15.7 - 1.99 * 1.08 = 13.55 = 13.6
Upper Limit = 15.7 + 1.99 * 1.08 = 17.85 = 17.9

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