find the margin of error for the sample proportion, given a sample size of n=1400. Round to the nearest percent.
To find the margin of error for the sample proportion, you need to know the desired level of confidence and the population proportion. Since you haven't provided the population proportion or the level of confidence, we'll assume a 95% level of confidence, which is commonly used for estimating margins of error.
When the sample size (n) is large, the standard formula for calculating the margin of error is:
Margin of Error = Z * sqrt((p * (1-p)) / n)
Where:
- Z is the z-score corresponding to the desired level of confidence.
- p is the estimated or assumed population proportion.
- n is the sample size.
Since you haven't provided the population proportion, we'll assume that it is 0.5, which is typically used when there is no information available about the population proportion.
Using the z-score value for a 95% level of confidence (Z = 1.96) and the sample size (n = 1400), we can calculate the margin of error as follows:
Margin of Error = 1.96 * sqrt((0.5 * (1-0.5)) / 1400)
Margin of Error ≈ 1.96 * sqrt(0.25 / 1400)
Margin of Error ≈ 1.96 * sqrt(0.00017857143)
Margin of Error ≈ 1.96 * 0.0133583836
Margin of Error ≈ 0.0261207422
Rounded to the nearest percent, the margin of error for the sample proportion is approximately 0.03 or 3%.
To find the margin of error for a sample proportion, you need to know the sample size (n). The formula to calculate the margin of error is:
Margin of Error = z * sqrt((p * (1-p)) / n)
Here is how to determine the margin of error given a sample size of n = 1400:
Step 1: Determine the desired level of confidence. The most common level of confidence is 95%. However, without this information, we will assume a 95% confidence level.
Step 2: Look up the critical z-score for the desired level of confidence. For a 95% confidence level, the z-score is approximately 1.96. This value corresponds to the 97.5th percentile of the standard normal distribution.
Step 3: Calculate the margin of error using the formula mentioned earlier:
Margin of Error = 1.96 * sqrt((p * (1-p)) / n)
Since the question doesn't provide any information about the sample proportion (p), we can assume a conservative estimate of 0.5 (maximum margin of error) to find the worst-case scenario.
Margin of Error = 1.96 * sqrt((0.5 * (1-0.5)) / 1400)
Step 4: Calculate the margin of error using a calculator or software:
Margin of Error ≈ 1.96 * sqrt(0.000178571)
Margin of Error ≈ 1.96 * 0.013362
Margin of Error ≈ 0.026148
Step 5: Finally, round the margin of error to the nearest percent:
Margin of Error ≈ 0.03 (rounded to the nearest percent)
Therefore, the margin of error, rounded to the nearest percent, for a sample proportion with a sample size of n = 1400 is approximately 3%.