Getting ready for the final, don't understand how to answer these

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Discussion Overview

The discussion revolves around determining the necessary sample size for estimating a population mean with a specified maximum error in the context of confidence intervals. Participants are exploring the mathematical relationship between sample size and error margin, particularly focusing on how to adjust sample size to achieve a desired level of precision.

Discussion Character

  • Homework-related
  • Mathematical reasoning

Main Points Raised

  • One participant seeks urgent help on predicting the required sample size for a given maximum error.
  • Another participant presents the formula for maximum error in estimating a mean and asks how much to increase the sample size to reduce the error to one-fifth its original size.
  • A subsequent post reiterates the question about the factor by which the sample size must increase, suggesting that it must be 5000.
  • A later reply confirms that the sample size must increase by a factor of 25, explaining that since $n$ is under a radical, this adjustment is necessary to achieve the desired error margin.

Areas of Agreement / Disagreement

There is no consensus on the correct sample size, as participants are discussing the calculations and assumptions involved without reaching a definitive conclusion.

Contextual Notes

The discussion does not clarify the initial sample size or the specific values of $\sigma$ and $E$, which may affect the calculations and assumptions made by participants.

chriskeller1
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Please please urgent help needed with questions like these

How do I predict how big the sample needs to be?

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Regarding confidence intervals for one mean or proportion, we are given that the maximum error $E$ of the estimate for $\mu$ is:

$$E=z_{\alpha/2}\cdot\frac{\sigma}{\sqrt{n}}$$

So, by what factor must $n$ increase so that $E$ is one-fifth as large?
 
MarkFL said:
Regarding confidence intervals for one mean or proportion, we are given that the maximum error $E$ of the estimate for $\mu$ is:

$$E=z_{\alpha/2}\cdot\frac{\sigma}{\sqrt{n}}$$

So, by what factor must $n$ increase so that $E$ is one-fifth as large?
n must be 5000 right?
 
chriskeller1 said:
n must be 5000 right?

Yes, because $n$ is under a radical, it must increase by a factor of $5^2=25$ in order for $E$ to be 1/5 as large. and so we find:

$$200\cdot25=5000$$
 

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