Find the minimum sample size required to estimate an unknown population mean using the given data.
Confidence Level: 90%
Margin of error = 1.923
σ= 30
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 = population standard deviation
E = margin of error
In this case, the given confidence level is 90% (which corresponds to a Z-score of 1.645), the margin of error is 1.923, and the population standard deviation is σ = 30.
Substituting these values into the formula:
n = (1.645 * 30 / 1.923)^2
n = (49.35 / 1.923)^2
n = 25.64^2
n ≈ 658.3696
From the formula, we can see that the minimum sample size required to estimate an unknown population mean with a confidence level of 90%, a margin of error of 1.923, and a population standard deviation of 30 is approximately 659. Therefore, we would need a sample size of at least 659.