11.1 power point

8/7/2019 11.1 Power Point

1/16

Significance Tests: The Basics

Section 11.1


2/16

What is a Significance Test?

A formal procedure for comparing observeddata with a hypothesis whose truth we want toassess.

The hypothesis is a statement about apopulation parameter.

The results of a test are expressed in terms of aprobability that measures how well the data

and the hypothesis agree.The reasoning of hypothesis tests, like that of

confidence intervals, is based on asking whatwould happen if we repeated the experiment or

sampling procedure many, many times.


3/16

Stating Hypotheses

Notation:

the null hypothesis: H0

the alternative hypothesis: Ha


4/16

Can You Please Hurry It Up?

Vehicle accidents can result in serious injuries to driversand passengers. When they do, someone usually calls 911.Police, firefighters, and paramedics respond to theseemergency calls as quickly as possible. Slow response times

can have serious consequences for accident victims. In caseof life-threatening injuries, victims generally need medicalattention within 8 minutes of the crash. Several cities havebegun to monitor paramedic response times. In one suchcity, the mean response time to all accidents involving life-threatening injuries last year was = 6.7 minutes with a

standard deviation of 2 minutes. The city manager sharesthis information with emergency personnel and encouragesthem to do better next year. At the end of the followingyear, the city manager selects an SRS of 400 calls involvinglife-threatening injuries and examines the response times.The sample mean was 6.48 minutes. Do these data provide

good evidence that response times have decreased sincelast year?


5/16

If response times have not decreased, the mean response

time for 400 calls will have this sampling distribution. If the

result had been 6.61 minutes, that could easily happen just

by chance. But our results was so far out in the tail that it is

good evidence of a decrease in response times.


6/16

One Sided or Two ?

It that situation, we are seeking evidence of a

decrease in response time this year. The null

hypothesis would be that there is no decrease

and the alternative would be that there is adecrease.

H0: = 6.7 minutes

Ha: < 6.7 minutes

This is an example of a one-sided test because

we are interested only in deviations from the

null hypothesis in one direction.


7/16

If Youre Happy and You Know It

Does the job satisfaction of assembly workersdiffer when their work is machine-paced ratherthan self-paced? One study chose 18 subjects atrandom from a group of people who assembledelectronic devices. Half of the subjects wereassigned at random to each of two groups. Bothgroups did similar assembly work but one worksetup allowed workers to pace themselves, and

the other featured an assembly line that movedat fixed time intervals so that the workers werepaced by machine. After two weeks, all subjectstook the Job Diagnosis Survey, a test of jobsatisfaction. Then they switched work setups and

took the JDS again after two more weeks.


8/16

One Sided or Two ?

It that situation, we are seeking evidence

of a difference in JDS scores in the

population of all assembly workers.

H0: = 0

Ha: 0

This is an example of a two-sided test

because the direction of the difference

was not specified.


9/16

Some Cautions!

Hypotheses always refer to some population,

not to a particular outcome, so always state

the hypotheses in terms of the population

parameter, not the sample statistic.

The alternative hypothesis should express the

hopes or suspicions we have before we see thedata. It is cheating to first look at the data and

then create you hypotheses based n what the

data show.


10/16

Components of a Hypothesis Test For a

Population Mean (with known)

1. Name the procedure:

A hypothesis test for a population

mean ( known)

2. State the hypotheses and define any

symbols used:

H0: = _________

Ha: , or _________


11/16

3. Check the conditions:

S SRS from the population of

interest

I observations are independent

(N> 10n)

N population distribution is ~Northe sample size is large enough


12/16

4. Do the math:

Calculate the test statistic and find theassociated probability:

Is it always good to include a sketchthat illustrates the situation.

0 0( , , | | ) _____ x x

z P z or z

n n

Q Q

W W

! " !


13/16

P for Probability!

A P-value:


14/16


15/16

What Did You Just Say to Me?

This test (is/is not) statistically

significant since the P-value, ____, is

(>/


16/16

Statistical Significance

Significant in the

statistical sense does

not mean important.

It means simply not

likely to happen just

by chance.

11.1 power point

Documents