Assume that a standardized test is designed to have the mean score of 100 and the standard deviation of 15. At the 95% confidence interval, how large does the sample size have to be if the margin of error is to be 3 points?

Formula:

n = {[(z-value) * sd]/E}^2
...where n = sample size, sd = standard deviation, E = maximum error, and ^2 means squared.

Using the values you have in your problem:

n = {[(1.96) * 15]/3}^2

Calculate for sample size. Round your answer.

To determine the required sample size for a given margin of error at a specific confidence level, you 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 margin of error is 3 points, so E = 3.

To find the Z-score for a 95% confidence interval, we need to look up the value in a standard normal distribution table or use a calculator. For a 95% confidence level, the Z-score is approximately 1.96.

Substituting the given values into the formula, we have:

n = (1.96 * 15 / 3)^2
n = (29.4 / 3)^2
n = (9.8)^2
n = 96.04

Therefore, the sample size should be at least 97 (rounded up) in order to achieve a 95% confidence level with a margin of error of 3 points.

To determine the sample size required for a given margin of error at a specific confidence interval, 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, we want to find the sample size required to have a margin of error of 3 points at a 95% confidence interval.

Step 1: Find the z-score corresponding to a 95% confidence level.
To find the z-score, we can use a standard normal distribution table or a statistical calculator. For a 95% confidence interval, the z-score is approximately 1.96.

Step 2: Plug the values into the formula.
n = (1.96 * 15 / 3)^2
n = (5.88)^2
n ≈ 34.57

Step 3: Round off to the next whole number.
Since you cannot have a fractional sample size, round up the result to the next whole number.
n = 35

Therefore, the sample size required to have a margin of error of 3 points at a 95% confidence interval is 35.