Question

The following table shows site type and type of pottery for a random sample of 628 sherds at an archaeological location.

	Pottery Type
Site Type	Mesa Verde Black-on-White	McElmo Black-on-White	Mancos Black-on-White	Row Total
Mesa Top	72	64	53	189
Cliff-Talus	85	75	53	213
Canyon Bench	90	72	64	226
Column Total	247	211	170	628

Use a chi-square test to determine if site type and pottery type are independent at the 0.01 level of significance.

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

here null hypothesis:Ho:  site type and pottery type are independent

alternate hypothesis: Ha: site type and pottery type are dependent

applying chi square test of independence:

Expected	Ei=Σrow*Σcolumn/Σtotal	Mesa Verde	McElmo	Mancos	Total
	Mesa Top	74.34	63.50	51.16	189
	Cliff Talus	83.78	71.57	57.66	213
	Canyon Bench	88.89	75.93	61.18	226
	Total	247	211	170	628
chi square    χ2	=(Oi-Ei)2/Ei	Mesa Verde	McElmo	Mancos	Total
	Mesa Top	0.0734	0.0039	0.0660	0.143
	Cliff Talus	0.0179	0.1648	0.3765	0.559
	Canyon Bench	0.0139	0.2037	0.1301	0.348
	Total	0.105	0.372	0.573	1.050

  chi-square statistic for the sample =1.050

degree of freedom(df) =(rows-1)*(columns-1)=

4

as test statisitc is not signifcantly high; we can not reject null hypothesis.