Question

In a city, the racial make up is 68% White, 24% Black, 5% Asian and the remainder are classified as Other. A report on traffic stops by police officers in this city is being used to determine if the racial makeup of the motorists stopped reflect the racial makeup of the city. The race of drivers stopped by police officers over a 4 month period is recorded in the table. Determine if there is sufficient evidence to warrant the claim that the racial makeup of drivers in traffic stops significantly differs from the city's racial makeup.

R

Race	White	Black	Asian	Other
Drivers	896	399	68	57

ace White Black Asian Other Drivers 896 399 68 57 At the 0.025 significance level, test the claim that the racial distribution of drivers stopped in traffic stops conforms to the city's distribution of races.

The test statistic

is χ2=

The p-value is T

he conclusion is A. There is sufficient evidence to claim the racial makeup of drivers pulled over in traffic stops does not reflect the racial makeup of the city. B. There is not sufficient evidence to claim the racial makeup of drivers pulled over in traffic stops does not reflect the racial makeup of the city

Answer 1

Null Hypothesis : H_o : The racial distribution of drivers stopped in traffic stops conforms to the city's distribution of races

Alternate Hypothesis : H_a:  The racial distribution of drivers stopped in traffic stops does not conform to the city's distribution of races

Where O : Observed Frequency

E : Expected Frequency

Race	White	Black	Asian	Other	Total
Drivers:Observe Frequency	896	399	68	57	1420
City Racial Makeup	68%	24%	5%	100-68-24-5 =3	%

Expected frequency : City Racial makeup percentage x Total number drivers.

Race	White	Black	Asian	Other	Total
Drivers: Observe Frequency :O	896	399	68	57	1420
City Racial Makeup	68%	24%	5%	3%
Expected Frequnecy: E	68% of 1420	24% of 1420	5% of 1420	3% of 1420
Expected Frequnecy: E	965.6	340.8	71	42.6	1420

O	E	O-E	(O-E)2	(O-E)2/E
896	965.6	-69.6	4844.16	5.016735708
399	340.8	58.2	3387.24	9.939084507
68	71	-3	9	0.126760563
57	42.6	14.4	207.36	4.867605634
			Total	19.95018641

=19.95019

Degrees of freedom = Number of Categories -1 = 4-1 = 3

p-Value = P( > Test Statistic ) = P( > 19.95019) = 0.00017

Level of significance : = 0.05

As p-value : 0.00017 < : 0.05 ; Reject null hypothesis ;

Therefore,

The conclusion is
A. There is sufficient evidence to claim the racial makeup of drivers pulled over in traffic stops does not reflect the racial makeup of the city.