In: Statistics and Probability
We have 30 cross-validation results as below: 0.81, 0.20, 0.92, 0.99, 0.75, 0.88, 0.98, 0.42, 0.92, 0.90, 0.88, 0.72, 0.94, 0.93, 0.77, 0.78, 0.79, 0.69, 0.91, 0.92, 0.91, 0.62, 0.82, 0.93, 0.85, 0.83, 0.95, 0.70, 0.80, 0.90 Calculate the 95% confidence interval of the mean.
Let us first find mean and standard deviation for the given data
Sample mean is
And standard deviation is
Create the following table.
data | data-mean | (data - mean)2 |
0.81 | -0.0036999999999999 | 1.3689999999999E-5 |
0.20 | -0.6137 | 0.37662769 |
0.92 | 0.1063 | 0.01129969 |
0.99 | 0.1763 | 0.03108169 |
0.75 | -0.0637 | 0.00405769 |
0.88 | 0.0663 | 0.00439569 |
0.98 | 0.1663 | 0.02765569 |
0.42 | -0.3937 | 0.15499969 |
0.92 | 0.1063 | 0.01129969 |
0.90 | 0.0863 | 0.00744769 |
0.88 | 0.0663 | 0.00439569 |
0.72 | -0.0937 | 0.00877969 |
0.94 | 0.1263 | 0.01595169 |
0.93 | 0.1163 | 0.01352569 |
0.77 | -0.0437 | 0.00190969 |
0.78 | -0.0337 | 0.00113569 |
0.79 | -0.0237 | 0.00056169 |
0.69 | -0.1237 | 0.01530169 |
0.91 | 0.0963 | 0.00927369 |
0.92 | 0.1063 | 0.01129969 |
0.91 | 0.0963 | 0.00927369 |
0.62 | -0.1937 | 0.03751969 |
0.82 | 0.0063 | 3.969E-5 |
0.93 | 0.1163 | 0.01352569 |
0.85 | 0.0363 | 0.00131769 |
0.83 | 0.0163 | 0.00026569 |
0.95 | 0.1363 | 0.01857769 |
0.70 | -0.1137 | 0.01292769 |
0.80 | -0.0137 | 0.00018769 |
0.90 | 0.0863 | 0.00744769 |
Find the sum of numbers in the last column to get.
Hence standard deviation is
Now t table value 29 df for 95% CI is TINV(0.05,29)=2.045
So Margin of Error is
Hence CI is