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	87	48	135
B	90	55	145
C	74	80	154
Column Total	251	183	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.)

(c) What are the degrees of freedom?

(d) Find or estimate the P-value of the sample test statistic. (Round your answer to three decimal places.)

(e) 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.

Answer 1

The statistical software output for this problem is:

Contingency table results:
Rows: Ceremonial Ranking
Columns: None

	Cooking Jar Sherds	Decorated Jar Sherds (Noncooking)	Total
A	87	48	135
B	90	55	145
C	74	80	154
Total	251	183	434

Chi-Square test:

Statistic	DF	Value	P-value
Chi-square	2	9.5282422	0.0085

Hence,

a) Level of significance = 0.05

b) Chi - square statistic = 9.528

c) Degrees of freedom = 2

d) P - value = 0.009

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