8/6/2019 CU(S7)_St_Hyp(1)

1/13

truth Decision about H0

null hypothesisis true

null

hypothesis is

false

Type I errorHe is themurderer

He is not the

murderer

wrong decision right decision

right decision wrong decision

Type II error

reject H0 accept H0

8/6/2019 CU(S7)_St_Hyp(1)

2/13

production

process from

a machine

Case 1 To stop or not to stop

Past experience shows that, 5 percent of the items turned outby the machine are defective.

Each day the first 25 items produced by the machine are

inspected for defects. If 2 or fewer defects are found,

production is continued without interruption.If 2 or fewer defects are found, production is continued

without interruption. If 3 or more items are found to be

defective, production is interrupted and an engineer is asked

to adjust the machine. After adjustments have been made,

production is resumed.

8/6/2019 CU(S7)_St_Hyp(1)

3/13

Interpreting the quality control procedure described above as

a test of hypothesis, H0: T = 0.05 against H1: T > 0.05, T being

the population % of defective items.

The 4 possible courses of action are:

A.justified production stoppage to carry out machineadjustments.

B. an unnecessary interruption of production.

C. the continued production of an excess of defective items.

D. the continued production, without interruption, of itemsthat satisfy the accepted standard.

In test terminology, the engineer is asked to make

adjustments only when the hypothesis is rejected.

Draw the error table of testing of hypotheses and insert the

above courses of actions in the appropriate cells.

Determine which of the two errors is more detrimental.

8/6/2019 CU(S7)_St_Hyp(1)

4/13

truth decision

right decision

nullhypothesis is

true

H0:p = 0.05

null

hypothesis isfalse

H1:p > 0.05

Type I error

Type II errorright decision

the continued

production, without

interruption, of

items that satisfythe accepted

standard D

an unnecessary

interruption of

production

B

justified

production

stoppage to carry

out machine

adjustments A

the continued

production of an

excess of

defective items

C

?

?

8/6/2019 CU(S7)_St_Hyp(1)

5/13

truth decision

right decision

null hypothesis

true

H0: RAIN

null hypothesis

false

H1

: NO RAIN

Type I error

Type II errorright decision

A. Get wet in rain for not having an umbrella

B. Thank God, I did not carry an umbrella unnecessarily

C. I looked so silly carrying an umbrella in vainD. Saved from getting wet in rain

D

CB

A

?

?

8/6/2019 CU(S7)_St_Hyp(1)

6/13

State Highway Patrol periodically samples vehicle speeds at

various locations on a particular roadway to test if the

average speed limit crosses the danger level of 70 km per hr.

Radar traps are put in the locations which are designated as

danger zones.

A. Unnecessary insertion of radar traps.

B. Accidents due to speeding vehicles.C. ?

D. ?

Reject Null Hypothesis Accept Null Hypothesis

Null Hypothesis

is true

Null Hypothesisis false

null hypothesis H0:

alternative hypothesis H1:

Average speed limit = Q = 70

Q > 70

A

BD

C

Rightfully no radar traps are inserted

Radar traps are rightfully inserted

?

?

8/6/2019 CU(S7)_St_Hyp(1)

7/13

Given a choice we would definitely NOT commit ERRORS

But an errormay be there in a DECISION

We may at best try to MINIMISE the CHANCES OF

COMMITTING THE ERRORS

Type I error

$ REJECTING H0 when it is TRUE

Type II error

$ ACCEPTING H0 when it is FALSE

8/6/2019 CU(S7)_St_Hyp(1)

8/13

Probability of ( )

Type I errorProbability of ( )

Type II error

=E

=F

= size of the test

= significancelevel of the test

1 - F= power of the test

What is the practical interpretation of saying that the

significance level of the test is 0.05?

Pr (Type I error) = 0.05

Pr (REJECTING H0 when it is TRUE) = 0.05

8/6/2019 CU(S7)_St_Hyp(1)

9/13

The chances of both the errors can NOT be simultaneously

minimised.

So, we are left with no choice but to decide which of the two

chances we would like to minimise.

Either Type I error or Type II error could be the more crucial

one - according to the situation.

There is NO hard and fast rule dictating which is to be

minimised.

Conventionally, E is held constant at a low level

(= 0.10, 0.05, 0.01)

- the test is designed in such a way that F gets reduced

8/6/2019 CU(S7)_St_Hyp(1)

10/13

Hypothesis

It is a conjecture / guess / belief about a single / double /

multiple population. The hypothesis is about

population parameter

population distribution

some other attribute about population(s).

Null Hypothesis

H0 represents a conjecture / guess / belief that has been putforward, either because it is believed to be true or because it

is to be used as a basis for argument, but has not been

proved yet.

8/6/2019 CU(S7)_St_Hyp(1)

11/13

The term null is used because it is a hypothesis, the validity

of which, we wish to disprove or nullify against a alternative

hypothesis.

Alternative Hypothesis

When we disprove or nullify the null hypothesis , we do so

in favour of another assertion, which we term as alternativehypothesis.

The alternative hypothesis can be a negation of the null

hypothesis, or can also be precisely defined.

In conventional hypothesis testing, the null

hypothesis is written as a simple hypothesis.

8/6/2019 CU(S7)_St_Hyp(1)

12/13

One-sided Test

A one-sided test is a hypothesis test, in which the values for

which we can reject the null hypothesis, H0 are locatedentirely in one tail of the probability distribution of the test

statistic.

In other words, the critical region for a one-sided test is the

set of values less than the critical value of the test, or the set

of values greater than the critical value of the test.

H1: p > 0.05

8/6/2019 CU(S7)_St_Hyp(1)

13/13

Two-Sided Test

A two-sided test is a hypothesis test, in which the values for

which we can reject the null hypothesis, H0 are located in

both tails of the probability distribution of the test statistic.

In other words, the critical region for a two-sided test is the

set of values less than the left-sided critical value of the test

and the set of values greater than the right-sided critical

value of the test.

H1: p { 0.05