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	90	45	135
B	93	52	145
C	76	78	154
Column Total	259	175	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?

State the null and alternate hypotheses.

H₀: Ceremonial ranking and pottery type are independent.

H₁: Ceremonial ranking and pottery type are not independent.

H₀: Ceremonial ranking and pottery type are not independent.

H₁: Ceremonial ranking and pottery type are independent.    

H₀: Ceremonial ranking and pottery type are independent.

H₁: Ceremonial ranking and pottery type are independent.

H₀: Ceremonial ranking and pottery type are not independent.

H₁: Ceremonial ranking and pottery type are not independent.

(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.)

Are all the expected frequencies greater than 5?

Yes

No    

What sampling distribution will you use?

Student's t

uniform    

normal

chi-square

binomial

What are the degrees of freedom?

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

p-value > 0.100

0.050 < p-value < 0.100    

0.025 < p-value < 0.050

0.010 < p-value < 0.025

0.005 < p-value < 0.010

p-value < 0.005

(d) 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.

(e) Interpret your conclusion in the context of the application.

At the 5% level of significance, there is sufficient evidence to conclude that ceremonial ranking and pottery type are not independent.

At the 5% level of significance, there is insufficient evidence to conclude that ceremonial ranking and pottery type are not independent.

Answer 1

a ) the level of significance is 0.05

H₀: Ceremonial ranking and pottery type are independent.

H₁: Ceremonial ranking and pottery type are not independent.

Chi-Square Test for Association: Ceremonial Ranking, Worksheet columns

Rows: Ceremonial Ranking Columns: Worksheet columns

Cooking Decorated
Jar Jar Sherds
Sherds (Noncooking All

A 90 45 135
80.56 54.44
1.105 1.635

B 93 52 145
86.53 58.47
0.483 0.715

C 76 78 154
91.90 62.10
2.752 4.073

All 259 175 434

Cell Contents: Count
Expected count
Contribution to Chi-square

Pearson Chi-Square = 10.764, DF = 2, P-Value = 0.00459

b ) the value of chi square statistic is 10.764

yes all expected frequency are greater than 5

normal sampling distribution we will use here

the degree of freedom is 2

c ) the p value is 0.005

p-value < 0.005

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

e )At the 5% level of significance, there is sufficient evidence to conclude that ceremonial ranking and pottery type are not independent.