Question

What is the critical value t' for constructing a 90% confidence interval for a mean from a sample size of

n=18 observations?

Answer 1

`t^* = 1.740`

Step-by-step explanation:

Given

`n = 18` --- sample

`CI= 90\%` --- confidence interval

Required

Determine the critical value

Start by calculating the degrees of freedom (df)

`df = n - 1`

`df = 18 - 1`

`df = 17`

Next, calculate the significance level

`\alpha = (1 - CI)/(2)`

This gives:

`\alpha = (1 - 90\%)/(2)`

Express percentage as decimal

`\alpha = (1 - 0.90)/(2)`

`\alpha = (0.10)/(2)`

`\alpha = 0.05`

Next, we look at the t table at

`df = 17`

and

`\alpha = 0.05`

We have the critical value to be:

`t^* = 1.740`