Question

2) For a one-tailed hypothesis using a z-distribution, find the critical value (z-score) that will give you a critical region with an alpha of the following values:

a) alpha = 0.20

b) alpha = 0.10

c) alpha = 0.05

d) alpha = 0.01

e) alpha = 0.001

Answer 1

SolutionA:

z scores are with mean=0 and standard deviation=1

Install tigerstats library in R to get the z value and normal curve

Rcode is

library(tigerstats)
qnormGC(0.20,region="above",mean=0,sd=1,graph=TRUE)

output:

0.8416212

critical z score

=.84

a) alpha = 0.20 ,z=0.84

SolutionB:

qnormGC(0.10,region="above",mean=0,sd=1,graph=TRUE)

output:

1.281552

z=1.28

For alpha = 0.10,z=1.28

Solutionc:

qnormGC(0.05,region="above",mean=0,sd=1,graph=TRUE)

output:

1.644854

For alpha = 0.05,z=1.64

Solutiond:

qnormGC(0.01,region="above",mean=0,sd=1,graph=TRUE)

output:

2.326348

For alpha=0.01,z=2.33

Solutione:

e) alpha = 0.001

qnormGC(0.001,region="above",mean=0,sd=1,graph=TRUE)

output:

3.090232

For alpha=0.001,z=3.09