Statistics Confidence Intervals Question?

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SUMMARY

The discussion centers on the calculation of the margin of error for a Gallup Poll that surveyed 1002 adults, revealing that 25% experienced crime in the past year, with 43% among those aged 18-29. The margin of error for the total sample is +/- 3 percentage points at a 95% confidence level. Participants debate whether the margin of error for the younger demographic is larger due to a smaller sample size, and the need to calculate the required sample size for a similar confidence interval is highlighted.

PREREQUISITES
  • Understanding of confidence intervals and margin of error
  • Familiarity with sample size calculations in statistics
  • Knowledge of polling methodologies and sampling techniques
  • Basic statistical concepts such as population proportion
NEXT STEPS
  • Learn how to calculate margin of error for different sample sizes
  • Study the formula for determining sample size for a given confidence interval
  • Explore the implications of sample size on statistical precision
  • Investigate the impact of demographic factors on polling results
USEFUL FOR

Students studying statistics, researchers conducting surveys, and professionals in data analysis who need to understand confidence intervals and margin of error calculations.

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Homework Statement


A Gallup Poll of 1002 adults in October 2002 found that 25% of the respondents said that their household
had experienced a crime in the past year. Among respondents aged 18-29 years, 43% had been victims of a
crime. Gallup says, “For results based on the total sample of national adults, one can say with 95%
confidence that the margin of sampling error is +/- 3 percentage points.” Is the margin of error for adults
aged 18-29 smaller than, larger than, or the same as +/- 3 percentage points?


Homework Equations





The Attempt at a Solution


Well, I think because of the smaller sample size, the margin of error would be larger because it is less precise. Yet, this sample size comes from a larger sample size with a given confidence interval width, so I am not sure.
 
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Hi mintsapple!

Do you know how to calculate the confidence limit that Gallup provided? Can you calculate how big a sample of 18-24 year olds yu would need to get the same confidence interval?
 

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