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	84	51	135
B	93	52	145
C	74	80	154
Column Total	251	183	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 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.   

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

H₀: Ceremonial ranking and pottery type are independent.
H₁: Ceremonial ranking and pottery type are 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 or No    

What sampling distribution will you use?

uniform

Student's t    

binomialnormal

chi-square

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.   

Answer 1

(a) What is the level of significance?
Answer: Significance Level

Null Hypotheis and Alternative Hypothesis

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

b) The Calculation Table for expected frequencies are :

	Obs. Freq			Exp. Freq
Ceremonial Ranking	Cooking Jar Sherds	Decorated Jar Shreds	Row Total	Cooking Jar Sherds	Decorated Jar Shreds	Row Total
A	84	51	135	78.076	56.924	135
B	93	52	145	83.859	61.141	145
C	74	80	154	89.065	64.935	154
Column Total	251	183	434	251	183	434

Are all the expected frequencies greater than 5?

Answer: Yes

What sampling distribution will you use?

Answer: chi-square

What are the degrees of freedom?
Answer: (r-1)*(c-1) = (3-1)*(2-1) = 2*1 =2

The Calculation For Chi square test statistic is

	Obs. Freq ( f)	Exp. Freq ( e)	(f-e)2/e
	84	78.076	0.449
	51	56.924	0.617
	93	83.859	0.996
	52	61.141	1.367
	74	89.065	2.548
	80	64.935	3.495
Total	434	434	9.472

Under Ho, the test statistic is

c)  The P-Value is 0.009

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

Answer: Since the P-value ? ?, we reject the null hypothesis

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

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