If the population standard deviation is Ợ=8, how large a sample is necessary to have a standard error that is
a. Less than 4 points?
b. Less than 2 points?
c. Less than 1 point?
SEm = SD/√n = 4, 2 or 1
Plug in data and solve for n.
how would I find the n for this equation?
Thanks for the help I finally found out where I would receive my n from.
You are welcome.
To calculate the sample size necessary to achieve a specific standard error, we can use the formula:
n = (Z * σ / SE)²
Where:
- n represents the sample size
- Z is the Z-score corresponding to the desired level of confidence (e.g., 1.96 for a 95% confidence level)
- σ is the population standard deviation
- SE is the desired standard error
a. To find the sample size required when the standard error is less than 4 points:
n = (Z * σ / SE)²
n = (1.96 * 8 / 4)²
n = 3.92²
n ≈ 15.3664
Since the sample size should be a whole number, we can round up to the nearest whole number. Hence, a sample size of 16 is necessary.
b. To find the sample size required when the standard error is less than 2 points:
n = (Z * σ / SE)²
n = (1.96 * 8 / 2)²
n = 7.84²
n ≈ 61.4656
Again, rounding up to the nearest whole number, a sample size of 62 is necessary.
c. To find the sample size required when the standard error is less than 1 point:
n = (Z * σ / SE)²
n = (1.96 * 8 / 1)²
n = 15.68²
n ≈ 246.3424
Rounding up to a whole number, a sample size of 247 is necessary.