Hypothesis Testing Betsy Farber

8/11/2019 Hypothesis Testing Betsy Farber

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Chapter

7

Elementary Statistics

Larson Farber

Hypothesis Testing


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A Statistical Hypothesis

Alternative

hypothesis Hacontains a statement

of inequality, such as.

Null hypothesis H0Statistical hypothesis

hat contains a

tatement of equality,uch as , = or .

If I am false,you are true

If I am false,

you are true

H0Ha

Complementary Statements

A claim about a population.


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Write the claim about the population. Then,write its complement. Either hypothesis, the

ull or the alternative, can represent the claim

A hospital claims its ambulance responsetime is less than 10 minutes.

H0 : 10 min

Ha : 10 min claim

Ha :60.0

p

H0 : 60.0p claim

Writing Hypotheses

A consumer magazine claims theproportion of cell phone calls made during

evenings and weekends is at most 60%.


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A type I error:Null hypothesis is actually

rue but the decision is to reject it.

Level of significance,

Maximum probability of committing

a type I error.

Decisi

on

Actual Truth of H0

Errors and Level ofSignificance

H0 True H0 False

Do not

reject H0

Reject H0

Correct

Decision

Correct

Decision

Type II

Error

Type I

Error


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Sampling distribution for x

The rejection regionis the range of

values for which the null hypothesis is not

probable. It is always in the direction of

the alternative hypothesis. Its area is equalto a.

Rejection Region

0z z0

A critical valueseparates the rejection

region from the non-rejection region

Critical Value z0

Rejection Regions


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z00

-z0

0 z0

Right-tail test Ha:>valu

Reject H0if z > z0otherwise fail to reject H0.

Two-tail testHa:value

Reject H0ifz >z0 or z


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Claim is H0

There is not

enoughevidence to

reject the claim

There is

enoughevidence to

reject the claim

Interpreting the Decision


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Claim is Ha

There is not

enoughevidence to

support the

claim

There is

enoughevidence to

support the

claim

Interpreting the Decision


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1. Write the null and alternative hypothesi

2. State the levelof significance

3. Identify the sampling distribution

Write H0 and Haas mathematical statements.

Remember H0 always contains the = symbol.

This is the maximum probability of rejecting the

null hypothesis when it is actually true. (Makinga type I error.)

The sampling distribution is the distribution for

the test statistic assuming that H0 is true and

that the experiment is repeated an infinite

number of times.

8 Steps in a Hypothesis Test


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7. Make your decision

6.Find the test statistic

5.Find therejection region

4. Find thecritical value

8. Interpret your decision

The critical value separates the rejection region

of the sampling distribution from the non-

rejection region.

Perform the calculations to standardize your

sample statistic.

If the test statistic falls in the critical region,reject H0. Otherwise, fail to reject H0.


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The critical value z0separates the rejection region

rom the non-rejection region. The area of the

ejection region is equal to a.

z0 0

ejection

egion

z00

Rejection

region

-z0 0 z0

Rejection

region

Rejection

region

ind z0 for a left-tail

est with a=.01Find z0 for a right-tail

test with a=.05

Find - z0 and z

0for a two-tail test with a=.01

z0=-2.33

-z0=-2.575 and z0 =2.575

z0=1.645

Critical Values


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A cereal company claims the meansodium content in one serving of its cereal is

no more than 230 mg. You work fora

national health service and are asked to test

this claim. You find that a random sample of52 servings has a mean sodium content of

232 milligrams and a standard deviation of

10 mg. At a= 0.05, do you have enough

evidence to reject the companys claim?1. Write the null and alternative hypothesis

H0: 230 mg.(claim) Ha: > 230 mg.

2. State the level of significance

a= 0.05

3. Determine the sampling distribution

Since the sample size is at least 30, the sampling

distribution is normal.

The z-test for a Mean


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7. Make your decision

6. Find the test statistic

8. Interpret your decision

5. Find the rejection

region

Rejection

region

Since Hacontains the > symbol, this is a right tail tes

n=52

x = 232s=10

44.1

387.1

2

52

10

230232

z

= 1.44 does not fall in the rejection region, soail to reject H0

There is not enough evidence to reject the

ompanys claim that there is at most 230mg of

z00

1.645

4. Find the critical

value

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Hypothesis Testing Betsy Farber