Question

Bowl Sherds	Jar Sherds	Total
San Pedro	18	12	30
San Pablo	18	22	40
Total	36	34	70

Looking at the data, there seems to be disparity. Jar sherds seem much more frequent at San Pablo. But does this reflect a real difference in activities that took place, or simply sampling error? To answer this question, we need to frame the question as a set of testable hypotheses, select the appropriate statistic, and test whether these distributions are likely to be the result of sampling error, or alternatively represent a significant difference. Lets use 0.05 as our significance threshold. Based on this data set, answer the following questions:  

1. Calculate the expected values of the null hypothesis, and put these into a table.  

2. Calculate the Chi-Squared value for the observed data.

3.Calculate the degree of freedom

4. Look up the critical value using the Chi-Square critical value

Answer 1

1)

Expected	Ei=row total*column total/grand total	Bowl	jar	Total
	San pedro	15.429	14.571	30
	San pablo	20.571	19.429	40
	total	36	34	70

2)

Applying chi square test of independence:

chi square    χ2	=(Oi-Ei)2/Ei	Bowl	jar	Total
	San pedro	0.429	0.454	0.8824
	San pablo	0.321	0.340	0.6618
	total	0.7500	0.7941	1.544
test statistic X2 =		1.544

3)

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

1

4)

for 1 df and 0.05 level , critical value       χ2=

3.841