Question

Isaac, John A., and John L. of MyNek, MyBak and McCracton Conglomerate
were bored after Spring break, they consoled themselves by finding the critical
values for the following. (It’s possible!!)
a. C.L. = 97%, n is 25 and sigma is known.
b. C.L. = 95%, sample size is 30; find (σ is unknown, 2-tails).
c. the area in the left tail is 0.995, the sample size is 24

Answer 1

Solution:-

a) At 97% confidence level

= 1-0.97% =1-0.97 =0.03

/2 =0.03/ 2= 0.015

Z/2 = Z0.015 = 1.036

Z/2 = 1.036

critical value = 1.036

b)

sample size = n = 30

Degrees of freedom = df = n - 1 = 30 -1 = 29

At 95% confidence level

= 1-0.95% =1-0.95 =0.05

/2 =0.05/ 2= 0.025

t/2,df = t0.025,29 = 2.045

t /2,df = 2.045

c) This is a left tail test

= 0.995

sample size = n =24

Degrees of freedom = df = n - 1 = 24-1 = 23

critical value = -2.807