use the given information to find the minimum sample size required to estimate an unknown population mean. Margin of error/; $137, confidence level:99%, standard deviation = $535
Formula:
n = [(z-value * sd)/E]^2
...where n = sample size, z-value will be 2.58 using a z-table to represent the 99% confidence interval, sd = 535, E = 137, ^2 means squared, and * means to multiply.
Plug the values into the formula and finish the calculation. Round your answer to the next highest whole number.
To find the minimum sample size required to estimate an unknown population mean, given the margin of error, confidence level, and standard deviation, we can use the formula:
n = (Z * σ / E)^2
Where:
- n is the minimum sample size required
- Z is the Z-score corresponding to the desired confidence level
- σ (sigma) is the population standard deviation
- E is the margin of error
Given:
- Margin of error (E) = $137
- Confidence level = 99% (corresponding Z-score = 2.576)
- Standard deviation (σ) = $535
Applying the values into the formula:
n = (2.576 * 535 / 137)^2
Simplifying the equation:
n = (1404.44)^2
n ≈ 1970
Therefore, the minimum sample size required to estimate the unknown population mean is approximately 1970.
To find the minimum sample size required to estimate an unknown population mean, we can use the formula:
n = (Z * σ / E)^2,
where:
n = sample size
Z = Z-score corresponding to the desired confidence level
σ = standard deviation
E = margin of error
In this case, the given information is as follows:
Margin of error (E) = $137
Confidence level = 99% (which corresponds to a Z-score of 2.575)
Standard deviation (σ) = $535
Let's substitute these values into the formula:
n = (2.575 * $535 / $137)^2
To calculate the minimum sample size, we solve this equation:
n = (2.575 * $535 / $137)^2
n = (1394.125 / $137)^2
n = (10.187)^2
n ≈ 104
Therefore, the minimum sample size required to estimate the unknown population mean is approximately 104.