If the true population standard deviation was known to be 3, then approximately what minimum sample size would you need in an SRS (simple random sample) if you want a confidence interval for the margin of error of .5 or less?

To determine the minimum sample size needed for a confidence interval with a desired margin of error, we can use the formula:

n = (Z * σ / E)^2

Where:
n = sample size
Z = Z-value (corresponding to the desired confidence level)
σ = population standard deviation
E = margin of error

In this case, the population standard deviation (σ) is known to be 3, and the desired margin of error (E) is 0.5 or less. However, we need to know the desired confidence level in order to calculate the Z-value. The most common confidence level is 95% (Z = 1.96).

So, using the formula with the provided values:

n = (1.96 * 3 / 0.5)^2

Calculating this, we get:

n ≈ 69.984

Since we cannot have a fractional sample size, we round up to the next whole number. Therefore, the minimum sample size needed for an SRS with a population standard deviation of 3 and a desired margin of error of 0.5 or less is 70.