Binomial or Normal: Population Proportion Testing

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SUMMARY

This discussion centers on the methodology for testing population proportions using either the binomial distribution or the normal distribution. The original poster questions the applicability of the normal distribution given that the sample size is 20 and the product of the sample size and proportion (np) equals 9, which exceeds the threshold of 5. The consensus is that while the binomial method is appropriate, the normal approximation can be utilized under certain conditions, specifically when np and n(1-p) are both greater than 5.

PREREQUISITES
  • Understanding of binomial distribution
  • Knowledge of normal distribution and its properties
  • Familiarity with population proportion testing
  • Basic statistical concepts such as sample size and probability
NEXT STEPS
  • Study the conditions for using the normal approximation in binomial tests
  • Learn about the Central Limit Theorem and its implications for population proportions
  • Explore statistical software tools like R or Python for conducting proportion tests
  • Review case studies where both binomial and normal methods were applied to population proportion testing
USEFUL FOR

Statisticians, data analysts, students in statistics courses, and anyone involved in hypothesis testing related to population proportions will benefit from this discussion.

werson9339
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Homework Statement


This involve testing population proportion. (either small or big sample) this question is done by my lecturer by using binomial , i am wondering could it be done using normal distribution? because the np is 20(0.45) = 9 which is greater than 5 , https://www.flickr.com/photos/110120...6/15432962168

Homework Equations

The Attempt at a Solution

 
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werson9339 said:

Homework Statement


This involve testing population proportion. (either small or big sample) this question is done by my lecturer by using binomial , i am wondering could it be done using normal distribution? because the np is 20(0.45) = 9 which is greater than 5 , https://www.flickr.com/photos/110120...6/15432962168

Homework Equations

The Attempt at a Solution


Post the problem by typing it directly; I cannot open your link---I get a bad link message. Anyway, there are good reasons for NOT posting images; it is discouraged (although not outright forbidden) by PF. Read the pinned post 'Guidelines for students and helpers', by Vela.
 
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