Question

Find the t critical value ta/2 to calculate a 95% confidence interval for a population mean when the sample size is 17.

Answer 1

solution:

Degrees of freedom = df = n - 1 =17 - 1 = 16

a ) At 95% confidence level the t is ,

$\alpha$ = 1 - 95% = 1 - 0.95 = 0.05

  $\alpha$/ 2= 0.05 / 2 = 0.025

t$\alpha$ /2,df = t0.025,16 = 2.120 ( using student t table)

b.

Degrees of freedom = df = n - 1 =25 - 1 = 24

At 90% confidence level the t is ,

$\alpha$ = 1 - 90% = 1 - 0.90 = 0.1

$\alpha$ / 2 = 0.1 / 2 = 0.05

t$\alpha$ /2,df = t0.05,24 = 1.711 ( using student t table)