SOLUTION: A 99% confidence interval (in inches) for the mean height of a population is 65.7 < μ < 67.3. This result is based on a sample of size 144. Construct the 95% confidence interval.

Algebra ->  Probability-and-statistics -> SOLUTION: A 99% confidence interval (in inches) for the mean height of a population is 65.7 < μ < 67.3. This result is based on a sample of size 144. Construct the 95% confidence interval.      Log On


   

Question 1179095: A 99% confidence interval (in inches) for the mean height of a population is 65.7 < μ < 67.3. This
result is based on a sample of size 144. Construct the 95% confidence interval. (Hint: you will first
need to find the sample mean and sample standard deviation).
I'm struggling to find the mean and the standard deviation of this question.
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!

Hi
x̄ - ME < mu < x̄ + ME
A 99% confidence interval...
65.7 < μ < 67.3   | ME = (67.3-65.7)/2 = 1.6/2 = .8
x̄ = 66.5
ME =+z%2Asigma%2Fsqrt%28n%29
 .8 = +2.576%2Asigma%2F12
 (.8)(12) /2.576 = σ = 3.727

Construct the 95% confidence interval. 
ME =+z%2Asigma%2Fsqrt%28n%29 = 1.96*(3.727)/12 = .6 (rounded to nearest tenth)
x̄ - ME < mu < x̄ + ME
66.5 - .6 < mu < 66.5 +.6
  65.9  < mu < 67.1
Wish You the Best in your Studies.
 = CI	z = value
90%	z =1.645
92%	z = 1.751
95%	z = 1.96
98%	z = 2.326
99%	z = 2.576