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	88	47	135
B	96	49	145
C	81	73	154
Column Total	265	169	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?

(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.)

What are the degrees of freedom?

Answer 1

a)  level of significance = 0.05

b)

Observed Frequencies
	Cooking Jar Sherds	Decorated Jar Sherds	Total
A	88	47	135
B	96	49	145
C	81	73	154
Total	265	169	434
Expected Frequencies
	Cooking Jar Sherds	Decorated Jar Sherds	Total
A	265 * 135 / 434 = 82.4309	169 * 135 / 434 = 52.5691	135
B	265 * 145 / 434 = 88.5369	169 * 145 / 434 = 56.4631	145
C	265 * 154 / 434 = 94.0323	169 * 154 / 434 = 59.9677	154
Total	265	169	434
	(fo-fe)²/fe
A	(88 - 82.4309)²/82.4309 = 0.3763	(47 - 52.5691)²/52.5691 = 0.59
B	(96 - 88.5369)²/88.5369 = 0.6291	(49 - 56.4631)²/56.4631 = 0.9865
C	(81 - 94.0323)²/94.0323 = 1.8062	(73 - 59.9677)²/59.9677 = 2.8322

Test statistic:  

χ² = ∑ ((fo-fe)²/fe) = 7.220

degrees of freedom, df = (r-1)(c-1) = 2

Critical value:  

χ²α = CHISQ.INV.RT(0.05, 2) = 5.991

p-value:  

p-value = CHISQ.DIST.RT(7.220, 2) = 0.027  

Decision:  

p-value < α, Reject the null hypothesis.