Determine the minimum sample size required when you want to be

9595​%

confident that the sample mean is within one unit of the population mean and

sigmaσequals=12.612.6.

Assume the population is normally distributed.

Question content area bottom

Part 1

A

95 %95%

confidence level requires a sample size of

enter your response here.

To determine the minimum sample size required for a 95% confidence level, we can use the following formula for sample size \( n \):

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

Where:
- \( Z \) is the z-score corresponding to the desired confidence level (95% confidence level has a z-score of 1.96).
- \( \sigma \) is the population standard deviation (given as 12.6).
- \( E \) is the margin of error or the desired accuracy (given as 1 unit).

Let's compute the sample size:

\[
n = \left( \frac{1.96 \cdot 12.6}{1} \right)^2
\]

Now I'll calculate the value.The minimum required sample size is approximately 610.

Would you like further details or have any questions? Here are 5 related questions that can expand your understanding:

1. What would the sample size be if the margin of error was 0.5 instead of 1?
2. How would the sample size change if the confidence level increased to 99%?
3. What is the significance of the z-score in sample size determination?
4. How does a larger standard deviation affect the required sample size?
5. Why is it important to assume a normal distribution for this calculation?

**Tip**: Reducing the margin of error or increasing the confidence level will significantly increase the required sample size.

Determine the minimum sample size required when you want to be 95% confident that the sample mean is within one unit of the population mean, and the population standard deviation (σ) is 12.6. Assume the population is normally distributed.

Learn how to calculate the minimum sample size needed to achieve a 95% confidence level with a margin of error of 1 and a population standard deviation of 12.6. This tutorial explains key statistical concepts such as confidence intervals, normal distribution, and sample size determination. Suitable for undergraduate statistics students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation