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 need to use the formula:
Margin of Error = Critical Value * (Standard Deviation / √sample size)
1. Find the critical value for a 99% confidence level.
In this case, since the sample size is small (n = 15), you can use t-distribution instead of the z-distribution. The critical value for a 99% confidence level with 14 degrees of freedom (n-1) is obtained from the t-distribution table or using statistical software.
By looking up in the t-distribution table for 14 degrees of freedom and a confidence level of 99%, the critical value is approximately 2.977.
2. Calculate the margin of error.
Margin of Error = 2.977 * (7.92 / √15)
Using a calculator, first take the square root of 15 (√15), which is approximately 3.873. Then divide 7.92 by this value.
Margin of Error = 2.977 * (7.92 / 3.873)
Using a calculator, perform the division (7.92 / 3.873), which is approximately 2.043.
Margin of Error = 2.977 * 2.043
Using a calculator, multiply 2.977 by 2.043, which is approximately 6.086.
Therefore, the margin of error is approximately 6.086 (rounded to the nearest hundredth).
Keep in mind that this margin of error represents the maximum likely difference (positive or negative) between the sample mean and the population mean at a 99% confidence level.