Final answer:
To achieve a 95% confidence interval with a 4 point margin of error and a population standard deviation of 40, the required sample size is 154, after rounding up to the nearest whole number.
Step-by-step explanation:
To determine how large a sample should be selected to provide a 95% confidence interval with a margin of error of 4, when the population standard deviation is 40, we use the following formula for the sample size (n):
n = (Z* σ / E)^2
Where Z is the z-score corresponding to the desired confidence level, σ (sigma) is the population standard deviation, and E is the margin of error.
For a 95% confidence interval, the Z value is approximately 1.96. Plugging in the values, we have:
n = (1.96 * 40 / 4)^2
n = (49.6 / 4)^2
n = (12.4)^2
n = 153.76
After rounding up to the next whole number, we need a sample size of 154 to achieve our desired margin of error.