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 89 46 135

B 93 52 145

C 79 75 154

Column Total 261 173 434

Use a chi-square test to determine if ceremonial ranking and pottery type are independent at the 0.05 level of significance.

(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.

Answer 1

Hypothesis:-

  ceremonial ranking and pottery type are independent.

  ceremonial ranking and pottery type are dependent.

the necessary calculation table be:-

ceremonial ranking		pottery type		row total
		Cooking Jar Sherds	non-cooking Jar Sherds
A	obs freq (Oi)	89	45	135
	exp freq   (Ei)	(261*135)/434 =81.1866	53.8134
		0.7520	1.1345
B	obs freq (Oi)	93	52	145
	exp freq (Ei)	87.2005	57.7995
		0.3857	0.5819
C	obs freq (Oi)	79	75	154
	exp freq (Ei)	92.6129	61.3871
		2.6009	3.0187
column total		261	173	434

the test statistic be:-

df = (3-1)*(2-1) = 2

p value = 0.0195

[ in any blank cell of excel type =CHISQ.DIST.RT(7.874,2) press enter ]

d).decision:-

p value = 0.0195 <0.05 (alpha)

Since the P-value ≤ α, we reject the null hypothesis.

e).conclusion:-

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

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