The following table shows ceremonial ranking and type of pottery sherd for a ran

Question

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

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 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 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

uniform     

normal

binomial

Student's t

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.)


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

Since the P-value > ?, we fail to reject the null hypothesis.

Since the P-value > ?, we reject the null hypothesis.

Since the P-value ? ?, we reject the null hypothesis.

Since the P-value ? ?, we fail to reject the null hypothesis.

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

At the 5% level of significance, there is sufficient evidence to conclude that ceremonial ranking and pottery type are not independent.

At the 5% level of significance, there is insufficient evidence to conclude that ceremonial ranking and pottery type are not independent.

Ceremonial Ranking Cooking Jar Sherds Decorated Jar Sherds (Noncooking) Row Total A 85 50 135 B 91 54 145 C 76 78 154 Column Total 252 182 434

Explanation / Answer

a)

level of significance =0.05

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

applying chi square test of independence:

chi-square statistic =7.445

expected frequencies greater than 5 --Yes

sampling distribution will you use -chi square

degrees of freedom=(row-1)*(column-1)=(3-1)*(2-1)=2

c)

p vlaue =0.024

d)Since the P-value ? ?, we reject the null hypothesis.

e)

At the 5% level of significance, there is sufficient evidence to conclude that ceremonial ranking and pottery type are not independent.

Observed OBS cooking jar shreds Decorated Jar Total A 85 50 135 B 91 54 145 C 76 78 154 Total 252 182 434 Expected Ei=?row*?column/?total cooking jar shreds Decorated Jar Total A 78.387 56.613 135 B 84.194 60.806 145 C 89.4194 64.581 154 Total 252 182 434 chi square =(Oi-Ei)2/Ei cooking jar shreds Decorated Jar Total A 0.56 0.77 1.33 B 0.55 0.762 1.31 C 2.01 2.788 4.80 Total 3.12 4.32 7.445

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