Question

following data

safety injury severity	Fatal	non-fatal	no injuries	total
yes	669	155,071	467,362	623,102
no	487	4294	3824	8605
total	1,156	159,365	471,186	631,707

using this data, we wish to determine if there is any association between using safety restraints and injury severity. as such we will use a chi-square test for independence

Q10: state the null and alternative hypotheses

Q11:fill in the table below with the expected counts assuming the null hypothesis is true

safety restraint/injury severity	fatal	non-fatal	no injuries
yes
no

Q12: perform the chi-square test for independence at the .05 significance level.

Answer 1

we have given

safety injury severity	Fatal	non-fatal	no injuries	total
yes	669	155,071	467,362	623,102
no	487	4294	3824	8605
total	1,156	159,365	471,186	631,707

Ans 10_)the null and alternative hypotheses is

Statistics and Probability

following data

safety injury severity	Fatal	non-fatal	no injuries	total
yes	669	155,071	467,362	623,102
no	487	4294	3824	8605
total	1,156	159,365	471,186	631,707

Ans : the null and alternative hypotheses is

Ho: there is no association between using safety restraints and injury severity.

Ha: there is association between using safety restraints and injury severity.

using excel>addin>phstat>multiple sample test >chi square

we have

Chi-Square Test
Observed Frequencies
	Column variable			Calculations
saftey injury	fatel	non fatel	no injuries	Total		fo-fe
yes	669	155071	467362	623102		-471.253	-2123.16	2594.412
no	487	4294	3824	8605		471.2532	2123.158	-2594.41
Total	1156	159365	471186	631707
Expected Frequencies
	Column variable
saftey injury	fatel	non fatel	no injuries	Total		(fo-fe)^2/fe
yes	1140.253	157194.2	464767.6	623102		194.7634	28.67665	14.48245
no	15.74683	2170.842	6418.412	8605		14103.13	2076.523	1048.697
Total	1156	159365	471186	631707
Data
Level of Significance	0.05
Number of Rows	2
Number of Columns	3
Degrees of Freedom	2
Results
Critical Value	5.991465
Chi-Square Test Statistic	17466.27
p-Value	0
Reject the null hypothesis

Ans 11)

Expected Frequencies
	Column variable
saftey injury	fatel	non fatel	no injuries	Total
yes	1140.253	157194.2	464767.6	623102
no	15.74683	2170.842	6418.412	8605
Total	1156	159365	471186	631707

Ans 12 ) the value of chi-square test = 17466.27

p value is 0.0000 which is less than 0.05 so we reject Ho and conclude that there is association between using safety restraints and injury severity.