Final answer:
To construct a 95% confidence interval for the population mean with X=74, o=9, and n=60, calculate the standard error, multiply by the Z-score for 95% (1.96), and add/subtract from the sample mean to get the interval, which is (71.722, 76.278).
Step-by-step explanation:
To construct a 95% confidence interval estimate of the population mean when X=74, o=9, and n=60, you can use the formula for the confidence interval of the mean when the population standard deviation is known:
CI = µ ± Z*(σ/√n)
Where µ is the sample mean (X), σ is the population standard deviation (o), n is the sample size, and Z* is the Z-score corresponding to the desired confidence level. For a 95% confidence interval, the Z-score is typically 1.96.
First, calculate the standard error (SE):
SE = o / √n = 9 / √60 = 9 / 7.746 = 1.162
Then, multiply the standard error by the Z-score:
Margin of Error (ME) = Z* × SE = 1.96 × 1.162 = 2.278
Now, find the lower and upper bounds of the confidence interval:
Lower Bound = X - ME = 74 - 2.278 = 71.722
Upper Bound = X + ME = 74 + 2.278 = 76.278
The 95% confidence interval estimate for the population mean is (71.722, 76.278).