consider the following sample statistics from a population that is aproximatly normal. n=15, s= 7.92,level of confidence is 99 %
Calculate the margin of error( round to the nearest hunderth)
See previous post.
To calculate the margin of error, we can use the following formula:
Margin of Error = Critical Value * Standard Error
1. Firstly, let's find the critical value. Since the level of confidence is 99%, we need to determine the z-score associated with this confidence level.
To find the critical value, we can use a Z-table or a Z-score calculator. For a 99% confidence level, the critical value is approximately 2.576.
2. Next, we need to calculate the standard error. The standard error measures the variability of the sample mean and can be calculated using the formula:
Standard Error = (Sample Standard Deviation) / sqrt(n)
In this case, the sample standard deviation (s) is given as 7.92, and the sample size (n) is 15. Therefore:
Standard Error = 7.92 / sqrt(15)
3. Now, we can calculate the margin of error by multiplying the critical value and the standard error:
Margin of Error = 2.576 * (7.92 / sqrt(15))
Performing the calculations:
Margin of Error ≈ 2.576 * (7.92 / 3.87) ≈ 5.275
Therefore, the margin of error, rounded to the nearest hundredth, is approximately 5.28.