Question

Perform a​ chi-square homogeneity test. An independent simple random sample of residents in three regions gave the data on race shown in the table. At the

1 %1%

significance​ level, do the data provide sufficient evidence to conclude that a difference exists in race distributions among the three​ regions?

	White	Black	Other	Total
East	97	10	8	115
Midwest	116	17	4	137
West	117	15	13	145
Total	330	42	25	397

What are the null and alternative​ hypotheses?

A.

Upper H 0H0​:

The racial distribution is the same in at least two of the three regions.

Upper H Subscript aHa​:

The racial distribution is not the same in at least two of the three regions.

B.

Upper H 0H0​:

The racial distribution is the same in each of the three regions.

Upper H Subscript aHa​:

The racial distribution is not the same in each of the three regions.

C.

Upper H 0H0​:

The racial distribution is not the same in each of the three regions.

Upper H Subscript aHa​:

The racial distribution is the same in each of the three regions.

D.

Upper H 0H0​:

The racial distribution is not the same in at least two of the three regions.

Upper H Subscript aHa​:

The racial distribution is the same in at least two of the three regions.

Find the test statistic.

chiχ2equals=nothing

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

Find the​ P-value.

Pequals=nothing

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

Choose the correct conclusion below.

A.

Do not rejectDo not reject

Upper H 0H0.

The data

do not providedo not provide

sufficient evidence that there is a difference.

B.

RejectReject

Upper H 0H0.

The data

provideprovide

sufficient evidence that there is a difference.

C.

RejectReject

Upper H 0H0.

The data

do not providedo not provide

sufficient evidence that there is a difference.

D.

Do not rejectDo not reject

Upper H 0H0.

The data

provideprovide

sufficient evidence that there is a difference.

E.

At least one assumption is violated.​ Therefore, the test cannot be conducted.

Click to select your answer(s).

Answer 1

>> The null and alternative hypotheses: Option(B)

H0: The racial distribution is the same in each of the three regions.

Ha: The racial distribution is not the same in each of the three regions.

>> The test statistic:

χ^{​​​​​​2} = 5.191

>> The P-value:

P = 0.2683

>> The correct conclusion: Option(A)

Do not reject H0. The data do not provide sufficient evidence that there is a difference.

STATISTICAL OUTPUTS:

Actual Values:
97 10 8
116 17 4
117 15 13

Warning: Actual Value less than 5.
Results not reliable.

Expected Values:
95.5919 12.1662 7.24181
113.879 14.4937 8.6272
120.529 15.34 9.13098

Chi-Squared Values:
0.0207406 0.385709 0.0793788
0.0395002 0.433397 2.4818
0.103325 0.00753806 1.6394

Chi-Square Test Statistic = 5.19079

Degrees of Freedom = 4

P-value = 0.268276