Hypothesis Testing

Hypothesis Testing I

Pat Obi

What is a “Hypothesis?”
A statement or claim about the value of a population parameter: μ, σ2, p

Pat Obi, Purdue University Calumet

2

Decision Rule
1.

x  0
Z
s n Compare calculated Z value to Z value from
Table (critical Z value)


Reject H0 if calculated Z value lies in the rejection/significance region (i.e.  region)

ALTERNATIVELY:
2.

Compare p-value to 


Reject H0 if p-value < 
Pat Obi, Purdue University Calumet

3

Two-Tail Test



Ex: H0: 0 = 50; H1: 0 ≠ 50. Test at α = 0.05
Reject H0 if calculated Z is either less than ZCV on the left tail or greater than ZCV on the right
0

Rejection region: /2 = 0.025

Rejection region: /2 = 0.025

0
ZCV = -1.96

ZCV = 1.96
Pat Obi, Purdue University Calumet

4

One-Tail Test: Right/Upper Tail



Ex: H0: 0 ≤ 55; H1: 0 > 55. Test at α = 0.05
Reject H0 if calculated Z > Table Z (i.e. Zcv)
0

Rejection region:  = 0.05

ZCV = 1.645
Pat Obi, Purdue University Calumet

5

One-Tail Test: Left/Lower Tail



Ex: H0: 0 ≥ 12; H1: 0 < 12. Test at α = 0.05
Reject H0 if calculated Z < Table Z (i.e. Zcv)
0

Rejection region:  = 0.05

ZCV = -1.645
Pat Obi, Purdue University Calumet

6

Z Table (critical Z values)
Significance
Level


Zcv
One-Tail Test

Zcv
Two-Tail Test

0.10

1.285

1.645

0.05

1.645

1.960

0.01

2.326

2.576

Pat Obi, Purdue University Calumet

7

Rules Governing the Statement of
Hypothesis


In general,


The null hypothesis (H0) typically is a statement of equality or weak inequality (=, , )



Note that if the alternative hypothesis (HA) is true
(in that you rejected H0), then a corrective action may become necessary

Pat Obi, Purdue University Calumet

8

Some Useful Guidelines
1. What you wish to prove, or expect to conclude should be placed in the alternative. Some examples:
a. “You wish to prove that the average liquid content of a beverage is less than 64 fl oz”

H0: μ ≥ 64
[one-tail test]

H1: μ < 64
b. “Can we conclude that the