Question

Problem 3. Find the following quantities for ?= 0.1, 0.05, 0.01.

(a)z?/2

(b)t9,?/2, t15,?/2, t25,?/2

(c)?28,?/2, ?28,1??/2

Answer 1

The quantities can be found by respective tables or by simple R-commands.

(a) We have the following values as below.

For , we have , founded by command qnorm(0.1/2).

For , we have , founded by command qnorm(0.05/2).

For , we have , founded by command qnorm(0.01/2).

(b) For , we have

• , founded by command qt(0.1/2,df=9).
• , founded by command qt(0.1/2,df=15).
• , founded by command qt(0.1/2,df=25).

For , we have

• , founded by command qt(0.05/2,df=9).
• , founded by command qt(0.05/2,df=15).
• , founded by command qt(0.05/2,df=25).

For , we have

• , founded by command qt(0.01/2,df=9).
• , founded by command qt(0.01/2,df=15).
• , founded by command qt(0.01/2,df=25).

(c) For , we have

• , founded by command qchisq(0.1/2,df=8).
• , founded by command qchisq(1-(0.1/2),df=8).

For , we have

• , founded by command qchisq(0.05/2,df=8).
• , founded by command qchisq(1-(0.05/2),df=8).

For , we have

• , founded by command qchisq(0.01/2,df=8).
• , founded by command qchisq(1-(0.01/2),df=8).