Question

Which of the following confidence intervals has the largest critical value? 95% z-inteval or 95% t-interval with 18 degrees of freedom? Why?

Answer 1

solution:

z critical value

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.96   ( Using z table )

and

t critical value

n = Degrees of freedom = df = n - 1 =18 - 1 = 17

At 95% confidence level the t is ,

= 1 - 95% = 1 - 0.95 = 0.05

  / 2= 0.05 / 2 = 0.025

t /2,df = t0.025,17 = 2.1098 ( using student t table)

t critical value larger than z

when random sample less than 30 we use t critical value thats why critical value comes high compare to z