Question

Suppose you have selected a random sample of n=9 measurements from a normal distribution. Compare the standard normal zz= values with the corresponding t values if you were forming the following confidence intervals.

(a)    98% confidence interval
z=
t=

(b)    95% confidence interval
z=
t=

(c)    99% confidence interval
z=
t=

Answer 1

a)

   98% confidence interval :

z value =2.326 (from excel function: normsinv(0.99))

t =2.896 (from excel function :tinv(0.02,8))

b)

   95% confidence interval :

z value =1.96 (from excel function: normsinv(0.975))

t =2.306 (from excel function :tinv(0.05,8))

c)

   99% confidence interval :

z value =2.576 (from excel function: normsinv(0.995))

t =3.355 (from excel function :tinv(0.01,8))