Question

The 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	79	57	53	189
Cliff-Talus	76	71	66	213
Canyon Bench	97	68	61	226
Column Total	252	196	180	628

Use a chi-square test to determine if site type and pottery type are independent at the 0.01 level of significance.

(a) What is the level of significance?


State the null and alternate hypotheses.

H₀: Site type and pottery are not independent.
H₁: Site type and pottery are independent.

H₀: Site type and pottery are independent.
H₁: Site type and pottery are not independent.    

H₀: Site type and pottery are not independent.
H₁: Site type and pottery are not independent.

H₀: Site type and pottery are independent.
H₁: Site type and pottery 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?

normal

chi-square    

uniform

binomial

Student's t

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.)


(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 > ?, we fail to reject the null hypothesis.

Since the P-value > ?, we reject the null hypothesis.    

Since the P-value ? ?, we reject the null hypothesis.

Since the P-value ? ?, we fail to reject the null hypothesis.

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

At the 1% level of significance, there is sufficient evidence to conclude that site and pottery type are not independent.

At the 1% level of significance, there is insufficient evidence to conclude that site and pottery type are not independent.    

Answer 1

(a) What is the level of significance?

H0: Site type and pottery are independent.
H1: Site type and pottery are not independent.

(b) Find the value of the chi-square statistic for the sample.

Let's use excel for calculation

The formulae used on the above excelsheet are as follows:

Are all the expected frequencies greater than 5 ?

Yes, all the expected frequencies greater than 5

What sampling distribution will you use?

normal

chi-square    

uniform

binomial

Student's t

The correct option is Chi-square

What are the degrees of freedom? four

(c) Find or estimate the P-value of the sample test statistic.

p-value = 0.603

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis of independence?

Decision rule:

1) If p-value < level of significance (alpha) then we reject null hypothesis

2) If p-value > level of significance (alpha) then we fail to reject null hypothesis.

Here p value = 0.603 > 0.01 so we used 2nd rule.

That is we fail to reject null hypothesis

Since the P-value > ?, we fail to reject the null hypothesis.

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

At the 1% level of significance, there is insufficient evidence to conclude that site and pottery type are not independent.