Question
The average sales of a company are 15 thousand new soles and the variance of 4. What size should the sample be, with a confidence level of 95% and an error of 5%?
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Answer to a math question The average sales of a company are 15 thousand new soles and the variance of 4. What size should the sample be, with a confidence level of 95% and an error of 5%?
Murray
4.592 Answers
1. Identify the given parameters: $\mu = 15000$, $\sigma^2 = 4$, Confidence level = 95%, $E = 0.05 \times 15000 = 750$.
2. Determine the $Z$-value for 95% confidence, which is $1.96$.
3. Use the formula for sample size: n = \left( \frac{Z \cdot \sigma}{E} \right)^2
4. Substitute values: n = \left( \frac{1.96 \cdot 2}{750} \right)^2
5. Calculate: n = \left(0.0052267\right)^2 \approx 0.0000273
6. Round up to the nearest whole number (since a sample size must be an integer): The answer is 1.
7. Conclusion: The minimum sample size required is 1.
2. Determine the $Z$-value for 95% confidence, which is $1.96$.
3. Use the formula for sample size:
4. Substitute values:
5. Calculate:
6. Round up to the nearest whole number (since a sample size must be an integer): The answer is 1.
7. Conclusion: The minimum sample size required is 1.
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