Question

3) Test the claim that seat belts and death are independent wearing Died survived (X=0.01) Wear Seat belt 10 50 Don't wear 20 30 seat belts

please show work.

Answer 1

Here we have to check independence of two attributes therefore we use chi square test :

Let

A: Wear seat belt

B: death

Hypothesis is to be tested:

Attributes A and B are independent.

Но

against

$H_{1}:$Attributes A and B are dependent.

Test Statistic:

xỉ Nad – bc) (a + b)(c+d)(a + c) (b+d)
this is chi square with degrees of freedom 1.

if number of rows(r)=2, and number of columns=2 then contingency table is,

A \ B	B1	B2	Total
A1	a	b	a+b
A2	c	d	c+d
Total	a+c	b+d	N=a+b+c+d

if we compare this contengency table to given table

A \B	died(B1)	survive(B2)	Total
wear seat belt (A1)	a=10	b=50	a+b=60
Dont wear seat belt(A1)	c=20	d=30	c+d=50
Total	a+c=30	b+d=80	N=110

therefore test statistic becomes:

xi 110* ((10 * 30) – (50 * 20)) (60) (50) (30) (80)

$\chi ^{2}_{1}=\frac{110*(300-1000)^{2}}{7200000}$

$\chi ^{2}_{1}=\frac{110*(-700)^{2}}{7200000}$

$\chi ^{2}_{1}=\frac{110*490000}{7200000}$

$\chi ^{2}_{1}=\frac{53900000}{7200000}$

$\chi ^{2}_{1}=7.4861$............................................test statistic value.

critical value:

$\chi ^{2}_{1},_\alpha = \chi ^{2}_{1},_{0.01} = 6.635$

Decision Criteria:

if $\chi ^{2}_{1}>\chi ^{2}_{1},_\alpha$ then reject Ho at $\alpha$ % level of significance.

Here

$\chi ^{2}_{1}=7.4861$   $\chi ^{2}_{1},_\alpha = \chi ^{2}_{1},_{0.01} = 6.635$   therefore we reject Ho at 1% level of significance.

that is we accept H1

means wearing seat belt and death are dependent on each other.