Find the sample size that produces the margin of error +-4.0%
a) 325
b) 25
c) 16
d) 625
To find the sample size that produces a margin of error of +-4.0%, we need to use the formula:
n = (Z * σ / E)²
Where:
- n is the sample size
- Z is the Z-score (corresponding to the desired level of confidence)
- σ is the standard deviation (if known) or the estimated standard deviation
- E is the margin of error as a proportion (e.g., 0.04 for a +-4.0% margin of error)
Now, let's go through each option and calculate the sample size:
a) 325:
We need more information to calculate the sample size using option a). We don't have the value of σ or any other necessary information. Therefore, we cannot determine the sample size based on this option.
b) 25:
Again, we lack necessary information to calculate the sample size using option b). We don't have the value of σ or any other necessary information. Thus, we cannot determine the sample size for this option either.
c) 16:
Once more, we don't have sufficient information to calculate the sample size using option c). We lack the value of σ or any other necessary information. Therefore, we cannot determine the sample size for this option.
d) 625:
From the given option, we have a sample size of 625. However, still, we need more information. The value of σ or any other relevant information is not provided. Therefore, we cannot determine the sample size based on this option as well.
To correctly find the sample size that produces a margin of error of +-4.0%, we need more information such as the standard deviation or any other relevant data.