2. Standard error for the following data
5,6,7,8,9, Significance Level `alpha=0.05` and One-tailed test
Solution:
`bar x=7` and Variance `sigma^2=2.5` for `5,6,7,8,9`
| `x` | `x^2` |
| 5 | 25 |
| 6 | 36 |
| 7 | 49 |
| 8 | 64 |
| 9 | 81 |
| --- | --- |
| `sum x=35` | `sum x^2=255` |
Mean `bar x = (sum x)/n`
`=(5 + 6 + 7 + 8 + 9)/5`
`=35/5`
`=7`
Sample Variance `S^2 = (sum x^2 - (sum x)^2/n)/(n-1)`
`=(255 - (35)^2/5)/4`
`=(255 - 245)/4`
`=10/4`
`=2.5`
`sigma=sqrt(sigma^2)=sqrt(2.5)=1.5811`
Standard Error `=(sigma)/sqrt(n)=1.5811/sqrt(5)=1.5811/2.2361=0.7071`
This material is intended as a summary. Use your textbook for detail explanation.
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