Question

he 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	75	63	51	189
Cliff-Talus	82	68	63	213
Canyon Bench	94	72	60	226
Column Total	251	203	174	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.)

Answer 1

Hypotheses are:

H0:; The site type and pottery type are independent.

Ha:; The site type and pottery type are not independent.

Expected frequencies will be calculated as follows:

Following table shows the expected frequencies:

	Mesa Verde	McElmo	Mancos	Row total
Mesa Top	75.54	61.094	52.366	189
Cliff-Talus	85.132	68.852	59.016	213
Canyon Bench	90.328	73.054	62.618	226
Column Total	251	203	174	628

Following table shows the calculations for chi square test statistics:

O	E	(O-E)^2/E
75	75.54	0.003860207
82	85.132	0.115226049
94	90.328	0.149273581
63	61.094	0.059463057
68	68.852	0.010542962
72	73.054	0.015206779
51	52.366	0.035632968
63	59.016	0.268948353
60	62.618	0.109456131
Total		0.767610085

Following is the test statistics:

Degree of freedom: df =( number of rows -1)*(number of columns-1) = (3-1)*(3-1)=4

The p-value is: 0.9427

Since p-value is greater than 0.01 so we fail to reject the null hypothesis. That is we can conclude that  site type and pottery type are independent.

Excel function used for p-value: "=CHIDIST(0.77, 4)"