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 91 44 135 B 89 56 145 C 75 79 154 Column Total 255 179 434 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 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 not 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? binomial uniform chi-square normal 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.) 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 or fail to reject the null hypothesis of independence? Since the P-value > α, we fail to reject the null hypothesis. Since the P-value > α, we reject the null hypothesis. Since the P-value ≤ α, we reject the null hypothesis. Since the P-value ≤ α, 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.

Show formulas in excel if used please.

Answer 1

a)

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	79.320	55.680	134.9997235
	B	85.196	59.804	145
	C	90.484	63.516	154
	total	254.9997235	179	433.9997235
chi square    χ2	=(Oi-Ei)2/Ei	Ceremonial	Jar	Total
	A	1.720	2.450	4.1699
	B	0.170	0.242	0.4118
	C	2.650	3.775	6.4243
	total	4.5394	6.4666	11.006
test statistic X2 =		11.006

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)

from excel : p value =chidist(11.006,2) =0.004

p-value < 0.00

d)

Since the P-value ≤ α, 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