Question

You want to obtain a sample to estimate a population mean. Based on previous evidence, you believe the population standard deviation is approximately = 70.7. You would like to be 95% confident that your estimate is within 4.25 of the true population mean. How large of a sample size is required?

Do not round mid-calculation. Give your answer in whole people.
n =

Answer 1

To achieve a 95% confidence that the estimate is within 4.25 of the true population mean with a known standard deviation of 70.7, a sample size of 1079 is required.

Step-by-step explanation:

To calculate the required sample size to estimate a population mean with a specified margin of error and confidence level, we use the formula for the sample size of a mean:

n = (Z*σ/E)2

Where:

• n is the sample size
• Z is the Z-score corresponding to the desired confidence level
• σ is the population standard deviation
• E is the margin of error

For a 95% confidence level, the Z-score is approximately 1.96. Given that σ is 70.7 and the desired margin of error E is 4.25, we can plug these values into the formula:

n = (1.96*70.7/4.25)2 = (139.572/4.25)2 = 32.840242 = 1078.202

Since we cannot have a fraction of a person in the sample size, we round up to the nearest whole number:

n = 1079