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

CeremonialRanking	Cooking JarSherds	DecoratedJar Sherds (Noncooking)	RowTotal
A	81	54	135
B	94	51	145
C	77	77	154
ColumnTotal	252	182	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 arenot independent.
H₁: Ceremonial ranking and pottery type areindependent.   

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

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

(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?

normal

uniform     

binomial

Student's t

chi-square

What are the degrees of freedom?


(c) Find or estimate the P-value of the sample teststatistic. (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

(d) Based on your answers in parts (a) to (c), will you reject orfail to reject the null hypothesis of independence?

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.