Question

A random sample of n=25 is obtained from a population with variance σ^2, and the sample mean is computed. Test the null hypothesis H0 : μ = 110 versus the alternative hypothesis H1: μ>110 with α=0.01.

Compute the critical value (Xc overbar) and state your decision rule for the options below.

a.	The population variance is σ^2=256.
b.	The population variance is σ^2=400.
c.	The population variance is σ^2=900.
d.	The population variance is σ^2=500.

Answer 1

Ans:

critical z values=+/-2.576

a)standard error of mean=sqrt(256/25)=3.2

lower limit=110-2.576*3.2=101.76

upper limit=110+2.576*3.2=118.24

b)standard error of mean=sqrt(400/25)=4

lower limit=110-2.576*4=99.70

upper limit=110+2.576*4=120.30

c)

standard error of mean=sqrt(900/25)=6

lower limit=110-2.576*6=94.54

upper limit=110+2.576*6=125.46

d)

standard error of mean=sqrt(500/25)=4.472

lower limit=110-2.576*3.2=98.48

upper limit=110+2.576*3.2=121.52