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In measuring reaction time, a psychologist estimates that the standard deviation is 0.95 sec, how large a sample of measurements must be taken in order to be 95% confident that the error his estimate of mean will not exceed 0.01 second?...Solve simple don't use description 

To determine the sample size (\(n\)) required to achieve a specified margin of error (\(E\)) with a given confidence level, we can use the formula for the sample size of a mean:

\[ n = \left( \frac{Z \cdot \sigma}{E} \right)^2 \]

where:
- \(Z\) is the Z-score corresponding to the desired confidence level (for 95%, \(Z = 1.96\)),
- \(\sigma\) is the standard deviation,
- \(E\) is the margin of error.

Given:
- \(\sigma = 0.95\) seconds,
- \(E = 0.01\) seconds,
- \(Z = 1.96\) for a 95% confidence level.

Plugging in these values:

\[ n = \left( \frac{1.96 \cdot 0.95}{0.01} \right)^2 \]
\[ n = \left( \frac{1.862}{0.01} \right)^2 \]
\[ n = \left( 186.2 \right)^2 \]
\[ n = 34685.44 \]

Therefore, the sample size required is approximately:

\[ n \approx 34686 \]

The psychologist needs to take a sample of approximately 34,686 measurements to be 95% confident that the error in the estimate of the mean will not exceed 0.01 seconds.

Do you have any questions or need further details?

Here are 5 questions you can ask:
1. How do you calculate the Z-score for different confidence levels?
2. What is the margin of error in statistical estimation?
3. How is the standard deviation used in determining sample size?
4. Can you explain the concept of confidence intervals in statistics?
5. What are some common applications of sample size determination in research?

**Tip:** Always ensure your sample size is large enough to achieve the desired level of precision and confidence in your statistical estimates.

Learn how to calculate the sample size required for estimating the mean with a specified margin of error and confidence level. This problem involves statistical concepts such as sampling, standard deviation, and confidence intervals. Suitable for advanced undergraduate students and researchers.

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