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95% Confidence Interval for the population proportion

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The Friday after Thanksgiving is the biggest shopping day of the year. You are interested in the number of people who claim to have finished their Christmas shopping at the end of this weekend. On Monday, you take a random sample of people by standing at a toll booth at 7:00 a.m. and asking every third commuter if he or she has finished Christmas shopping. Based on the last year's data, you expect approximately 10% to claim completion of Christmas shopping. How many commuters must you sample of a 95% interval estimate to have a margin of error of +3%.

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Solution Summary

In this solution, it consists of detailed steps of finding a 95% confidence interval for the population proportion.

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Solution. The margin of error ME=3%=0.03, phat=10%=010. For a 95% confidence level, ...

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  • BSc , Wuhan Univ. China
  • MA, Shandong Univ.
Recent Feedback
  • "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
  • "excellent work"
  • "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
  • "Thank you"
  • "Thank you very much for your valuable time and assistance!"
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