Question

The following table shows ceremonial ranking and type of pottery sherd for a random sample of 434 sherds at an archaeological location.

Ceremonial Ranking Cooking Jar Sherds Decorated Jar Sherds (Noncooking) Row Total

A 89 46 135

B 93 52 145

C 79 75 154

Column Total 261 173 434

Use a chi-square test to determine if ceremonial ranking and pottery type are independent at the 0.05 level of significance.

(a) What is the level of significance?

State the null and alternate hypotheses.

H0: Ceremonial ranking and pottery type are independent. H1: Ceremonial ranking and pottery type are independent.

H0: Ceremonial ranking and pottery type are independent. H1: Ceremonial ranking and pottery type are not independent.

H0: Ceremonial ranking and pottery type are not independent. H1: Ceremonial ranking and pottery type are independent.

H0: Ceremonial ranking and pottery type are not independent. H1: Ceremonial ranking and pottery type are not independent.

(b) Find the value of the chi-square statistic for the sample. (Round the expected frequencies to at least three decimal places. Round the test statistic to three decimal places.)

Are all the expected frequencies greater than 5? Yes No

What sampling distribution will you use?

chi-square binomial normal Student's t uniform

What are the degrees of freedom?

(c) Find or estimate the P-value of the sample test statistic. (Round your answer to three decimal places.)

p-value > 0.100

0.050 < p-value < 0.100

0.025 < p-value < 0.050

0.010 < p-value < 0.025

0.005 < p-value < 0.010

p-value < 0.005

Answer 1

level of significance =0.05

H0: Ceremonial ranking and pottery type are independent. H1: Ceremonial ranking and pottery type are not independent.

b)

Applying chi square test of independence:

Expected	Ei=row total*column total/grand total	Ceremonial	Jar	Total
	A	81.190	53.813	135.0033641
	B	87.200	57.800	145
	C	92.613	61.387	154
	total	261.0033641	173	434.0033641
chi square    χ2	=(Oi-Ei)2/Ei	Ceremonial	Jar	Total
	A	0.751	1.134	1.8857
	B	0.386	0.582	0.9676
	C	2.001	3.019	5.0197
	total	3.1379	4.7351	7.873
test statistic X2 =		7.873

Are all the expected frequencies greater than 5? :Yes

What sampling distribution will you use? chi-square

degrees of freedom =(row-1)*(column-1)=2

c) p value =0.020

0.010 < p-value < 0.025