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posted by  wskr0313@hotmail.c on 10/19/2009 7:22:38 PM  |  status: Closed  |  Earned Karma: 57

Statistics help please, lifesaver rating

Course Textbook Chapter Problem Needs by
Statistics and Probability Elementary Statistics (10th) by Triola N/A N/A 10/20/2009 at 7:00:00 PM
Question Details:
A simple random sample of birth weights in the United States has a mean of 3433 g. The standard deviation of all birth weights is 495 g.
  1. Using a sample size of 75, construct a 95% confidence interval estimate of the mean birth weight in the United States.
  2. Using a sample size of 75,000, construct a 95% confidence interval estimate of the mean birth weight in the United States.
  3. Which of the preceding confidence intervals is wider? Why?

The answer is below but I would like help with the solution, thank you 

a. 3321 g < μ < 3545 g, b. 3429 g < μ < 3437 g, c. The confidence interval in a is wider. The smaller sample results in an estimate that is not as accurate.

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posted by Jonpp on 10/19/2009 8:44:33 PM  |  status: Live
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Response Details:
X-bar=3433, S=495

(a)n=75, α=0.05, Z(0.025)=1.96
The 95% confidence interval is X-bar±Z*s/√n-->3433±1.96*495/√75 --> (3320.971, 3545.029)

(b) n=75,000
The 95% confidence interval is 3433±1.96*495/√75000--->(3429.457, 3436.543)
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