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