How Large Should n Be for a Specific Confidence Interval Width?

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SUMMARY

The discussion centers on determining the minimum sample size n required for a 95% confidence interval width of at most 0.2, given a normal distribution with an unknown mean μ and a variance of 100. The calculation involves using the formula for the confidence interval length, which is influenced by the standard error derived from the sample size. Participants concluded that if the confidence interval width is doubled to 0.4, the sample size n must be increased to maintain the desired confidence level.

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  • Understanding of confidence intervals and their significance in statistics
  • Familiarity with normal distribution properties
  • Knowledge of sample size determination techniques
  • Basic statistical concepts such as mean, variance, and standard error
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  • Study the formula for confidence intervals in normal distributions
  • Learn about sample size calculations for different confidence levels
  • Explore the impact of variance on confidence interval width
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Statisticians, data analysts, researchers conducting hypothesis testing, and anyone involved in designing experiments requiring precise confidence intervals.

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You have a random sample of size n from a normal distribution with unknown mean μ and variance 100. You want to find n large enough so that the length of the confidence interval (from left endpoint to right endpoint) is at most .2. Find such a value of n so that n is as small as possible. If you instead were willing to have a confidence interval with twice this length, what would you need to do to n? (Note: All confidence intervals in this problem are 95 percent confidence intervals.)

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Looks right.
 
pasmith said:
Looks right.

Thanks :)
 

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