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A medical statistician wants to estimate the average weight loss of people who are on a...

A medical statistician wants to estimate the average weight loss of people who are on a new diet plan. In a study, he guesses that the standard deviation of the population of weight losses is about 20 pounds.

  1. How large a sample should he take to estimate the mean weight loss to within 8 pounds from the sample average weight, with 95% confidence?
  2. Is your estimation always correct? Please briefly explain your reasoning.
  3. If you start with a bigger sample, (under the condition that the confidence level and standard deviation remain unchanged,) then does it affect the accuracy of the estimation? Please briefly explain your reasoning.
  4. What happens to the confidence interval if the standard deviation takes a bigger value? Please briefly explain your reasoning.
Math   Statistics-And-Probability   
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