Question

# The following table shows ceremonial ranking and type of pottery sherd for a random sample of...

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 86 49 135 B 89 56 145 C 74 80 154 Column Total 249 185 434

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 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 not independent.     H0: Ceremonial ranking and pottery type are not independent.
H1: Ceremonial ranking and pottery type are not independent. H0: Ceremonial ranking and pottery type are independent.
H1: Ceremonial ranking and pottery type are 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 binomial     uniform normal chi-square

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.

The statistical software output for this problem is:

Hence,

a) Level of significance = 0.05

Hypotheses: H0: Ceremonial ranking and pottery type are independent.

H1: Ceremonial ranking and pottery type are not independent.

b) Test statistic = 8.635

Yes

Chi - square

Degrees of freedom = 3

c) 0.010 < p-value < 0.025

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.