You work for an insurance company and are studying the relationship between types of crashes and the vehicles involved. As part of your​ study, you randomly select

MATLAB: An Introduction with Applications
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Author:Amos Gilat
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You work for an insurance company and are studying the relationship between types of crashes and the vehicles involved. As part of your​ study, you randomly select

3632

vehicle crashes and organize the resulting data as shown in the contigency table. At

α=0.01​,

can you conclude that the type of crash depends on the type of​ vehicle? Complete parts​ (a) through​ (d).

 

Vehicle

 

Type of crash

Car

Pickup

Sport utility

​ Single-vehicle

876

393

342

​ Multiple-vehicle

1143

475

403

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Part 1

​(a) Identify the claim and state the null and alternative hypotheses.

H0​:

The type of crash and the type of vehicle are

 

.

Ha​:

The type of crash and the type of vehicle are

 

.


 (a) Identify the claim and state the null and alternative hypotheses.

H0​:

The type of crash and the type of vehicle are

Ha​:

The type of crash and the type of vehicle are

.

The

alternative hypothesis

 

is the claim.

Part 2

​(b) Determine the degrees of​ freedom, find the critical​ value, and identify the rejection region.

Part 3

Calculate the degrees of freedom.

d.f.=

Part 4

Find the critical value.

χ20=

​(Round to three decimal places as​ needed.)

Part 5

Which region below is the correct rejection​ region?

.

D.chi squared greater than or equals chi Subscript 0 Superscript 2

χ2≥χ20

Your answer is not correct.

Part 6

​(c) Calculate the test statistic. If​ convenient, use technology.

χ2=

​(Round to two decimal places as​ needed.)

Part 7

​(d) Decide to reject or fail to reject the null hypothesis. Then interpret the decision in the context of the original claim.

Part 8

What is the conclusion of the​ test?

 

H0.

There

 

enough evidence to support

Ha.

Part 9

How does this conclusion relate to the original​ claim?

A.

This

does not support

the claim that types of crash and vehicle are related.

.

B.

This

supports

the claim that types of crash and vehicle are related.

C.

This does not support the claim that types of crash and vehicle are not related.

D.

This supports the claim that types of crash and vehicle are not related.

 

 

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