Question

If you were constructing a 99% confidence interval of the population mean based on a sample of n 1) = 25 where the standard deviation of the sample S = 0.05, the critical value of t will be

Answer 1

We want a confidence of 99% so then the significance level would be 1%

The degrees of freedom are given by:

`df = n-1= 25-1=24`

And the critical value using the significance level
`\alpha=0.01` and
`\alpha/2 =0.005` and the critical value would be:

`t_(\alpha/2)= \pm 2.797`

Explanation:

We know the following info :

`s= 0.05` represent the standard deviation from the sample

`n = 25` represent the sample size selected

We want a confidence of 99% so then the significance level would be 1%

The degrees of freedom are given by:

`df = n-1= 25-1=24`

And the critical value using the significance level
`\alpha=0.01` and
`\alpha/2 =0.005` and the critical value would be:

`t_(\alpha/2)= \pm 2.797`