Question

If we aim to capture 95% of the sample statistic, what should be the corresponding margin of error?

A) ±1%
B) ±2%
C) ±5%
D) ±10%

Answer 1

To calculate the margin of error, we need to consider the desired level of confidence, critical value, and standard deviation of the sample statistic.

Step-by-step explanation:

To capture 95% of the sample statistic, we need to determine the corresponding margin of error. The margin of error is a measurement of the accuracy of the sample statistic and represents the maximum expected difference between the sample statistic and the true population parameter. To calculate the margin of error, we need to consider the desired level of confidence. In this case, we want a 95% confidence level.

To determine the corresponding margin of error, we can use the formula:
Margin of Error = Critical Value * Standard Deviation of the Sample Statistic

For a 95% confidence level, the critical value is approximately 1.96. If we assume the sample statistic follows a normal distribution, the standard deviation of the sample statistic can be calculated using a formula or estimated from the sample data. Once we have these values, we can calculate the margin of error.

Therefore, the correct choice for the corresponding margin of error would be option A) ±1%.

Answer 2

±5% should be the corresponding margin of error (option c).

Step-by-step explanation:

To capture 95% of the sample statistic, we use the concept of a margin of error in statistics. The margin of error is determined by calculating the critical value corresponding to the desired confidence level. For a 95% confidence level, which is a common choice, the critical value is approximately 1.96 (option c).

The margin of error is then calculated by multiplying this critical value by the standard deviation of the sample. Mathematically, it can be expressed as Margin of Error = Critical Value × Standard Deviation. In the context of a 95% confidence level, the margin of error is approximately 1.96 times the standard deviation.

Given the provided options, ±5% corresponds to a margin of error suitable for capturing 95% of the sample statistic. This aligns with the common practice in statistical analysis where a 95% confidence level is associated with a margin of error of approximately 5%, providing a reasonable balance between precision and reliability in estimating population parameters. Therefore, option C) ±5% is the correct choice for capturing 95% of the sample statistic.