Hypothesis Assessment I

Dab Obi

What exactly is " Hypothesis? ”

A statement or declare about the importance of a

human population parameter: μ, σ2, s

Pat Obi, Purdue University or college Calumet

two

Decision Secret

1 .

x 0

Z

h

n

Compare calculated Unces value to Z value from

Table (critical Z value)

Reject H0 if determined Z value lies in the

rejection/significance place (i. e. region)

ALTERNATIVELY:

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Compare p-value to

Reject H0 if p-value <

Dab Obi, Purdue University Pipe

3

Two-Tail Test

Ex lover: H0: 0 = 55; H1: 0 � 50. Test for α sama dengan 0. 05

Reject H0 if determined Z will either be less than ZCV

on the left butt or more than ZCV on the right

0

Rejection region: /2 sama dengan 0. 025

Rejection place: /2 sama dengan 0. 025

0

ZCV = -1. 96

ZCV = 1 ) 96

Terry Obi, Purdue University Calumet

4

One-Tail Test: Right/Upper Tail

Ex girlfriend or boyfriend: H0: 0 ≤ 55; H1: 0 > fifty-five. Test at α = 0. 05

Reject H0 if calculated Z > Table Unces (i. e. Zcv)

0

Rejection location: = 0. 05

ZCV sama dengan 1 . 645

Pat Obi, Purdue University Calumet

5

One-Tail Test out: Left/Lower Butt

Ex: H0: 0 ≥ 12; H1: 0 < 12. Test out at α = 0. 05

Decline H0 if calculated Z < Desk Z (i. e. Zcv)

0

Denial region: = zero. 05

ZCV = -1. 645

Dab Obi, Purdue University Pipe

6

Z . Table (critical Z values)

Significance

Level

Zcv

One-Tail Test out

Zcv

Two-Tail Test

zero. 10

1 ) 285

1 ) 645

zero. 05

1 ) 645

1 . 960

0. 01

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Pat Obi, Purdue University Houka

7

Guidelines Governing the Statement of

Hypothesis

In general,

The null hypothesis (H0) typically is a statement

of equality or weak inequality (=, , )

Note that in case the alternative hypothesis (HA) applies

(in that you rejected H0), then a corrective action

could become necessary

Pat Obi, Purdue University Houka

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Some Useful Recommendations

1 . Whatever you wish to prove, or be ready to conclude

should be placed in the alternative. Some examples:

a. " You would like to prove that the standard liquid content material of a drink is less than 64 fl oz”

H0: μ ≥ 64

[one-tail test]

H1: μ < sixty four

b. " Can we determine that the population mean can be NOT 150”?

H0: μ = 150

[two-tail test]

H1: μ � a hundred and fifty

c. " Can we conclude that the populace mean is usually GREATER than 150”?

H0: μ 150

[one-tail test]

H1: μ > one hundred and fifty

d. " Can we determine that a selected population indicate is LESS than 150”?

H0: μ 150

[one-tail test]

H1: μ < one hundred and fifty

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2 . In any two-tailed test, the null hypothesis (H0)

always goes with the equality. The alternate (HA)

hypothesis usually goes with the inequality:

" Are you able to concluded that the population is comparable to 70

percent? ”

H0: P sama dengan 0. 75

H1: L zero. 70

[two-tailed test]

Terry Obi, Purdue University Houka

10

three or more. The null hypothesis (H0) is a posted statement

or claim. Examples:

" A recent report on fresh IT firms states that the

average staff age in these companies is 27”

H0: μ = 28 [two-tailed test]

H1: μ 28

" A pharmaceutical firm claims that 80% of

physicians suggest a certain drug”

H0: S = 0. 80 [two-tail test]

H1: P 0. eighty

Pat Obi, Purdue University Calumet

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" A certain medication is considered powerful only if

the concentration of a specific chemical in it is

200ppm. At the same time, the medicine would

develop undesirable side effect if the attention

of the same chemical exceeds 200ppm. ” You are

worried about possible unwanted effects. Note that if perhaps

H0 is valid, no corrective action will have to be

made.

zero

H0: μ = two hundred

H1: μ > 2 hundred [one-tail test]

Pat Obi, Purdue School Calumet

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Speculation Testing: Intro

1 .

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3.

four.

Type 1 Error

Type 2 Problem

Power of Check

P-value

Terry Obi, Purdue University Pipe

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= P(Rejecting H0/H0 is usually true)

Type 1 Error

Wrongly reject H0 when in fact H0 applies

α = probability of rejecting H0 when H0 is true...