The following table shows ceremonial ranking and type of potterysherd for a random sample of 434 sherds at an archaeologicallocation.

Ceremonial Ranking	Cooking JarSherds	Decorated Jar Sherds(Noncooking)	RowTotal
A	91	44	135
B	96	49	145
C	81	73	154
ColumnTotal	268	166	434

Use a chi-square test to determine if ceremonial ranking andpottery 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 arenot independent.
H₁: Ceremonial ranking and pottery type are notindependent.

H₀: Ceremonial ranking and pottery type areindependent.
H₁: Ceremonial ranking and pottery type are notindependent.    

H₀: Ceremonial ranking and pottery type arenot independent.
H₁: Ceremonial ranking and pottery type areindependent.

H₀: Ceremonial ranking and pottery type areindependent.
H₁: Ceremonial ranking and pottery type areindependent.

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


Are all the expected frequencies greater than5?

Yes

No    

What sampling distribution will you use?

Student's t

uniform    

normal

chi-square

binomial

What are the degrees of freedom?


(c) Find or estimate the P-value of the sampletest statistic. (Round your answer to three decimalplaces.)

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

(d) Based on your answers in parts (a) to (c), will youreject or fail to reject the null hypothesis ofindependence?

Since the P-value > α, we fail to rejectthe null hypothesis.

Since the P-value > α, we reject the nullhypothesis.   

Since the P-value ≤ α, we reject the nullhypothesis.

Since the P-value ≤ α, we fail to reject thenull hypothesis.

(e) Interpret your conclusion in the context of theapplication.

At the 5% level of significance, there is sufficient evidence toconclude that ceremonial ranking and pottery type are notindependent.

At the 5% level of significance, there is insufficient evidenceto conclude that ceremonial ranking and pottery type are notindependent.