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	73	58	58	189
Cliff-Talus	80	66	67	213
Canyon Bench	87	64	75	226
Column Total	240	188	200	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 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.H₀: Site type and pottery are not 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?

uniform

binomial    chi-square

normal

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.)

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 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

Ans:

a)level of significance=0.01

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

b)

	Observed(fo)
Site Type	Mesa Verde	McElmo	Mancos	Row Total
	Black-on-White	Black-on-White	Black-on-White
Mesa Top	73	58	58	189
Cliff-Talus	80	66	67	213
Canyon Bench	87	64	75	226
Column Total	240	188	200	628
	Expected(fe)
Site Type	Mesa Verde	McElmo	Mancos	Row Total
	Black-on-White	Black-on-White	Black-on-White
Mesa Top	72.229	56.580	60.191	189
Cliff-Talus	81.401	63.764	67.834	213
Canyon Bench	86.369	67.656	71.975	226
Column Total	240	188	200	628
	Chi square=(fo-fe)^2/fe
Site Type	Mesa Verde	McElmo	Mancos	Row Total
	Black-on-White	Black-on-White	Black-on-White
Mesa Top	0.008	0.036	0.080	0.124
Cliff-Talus	0.024	0.078	0.010	0.113
Canyon Bench	0.005	0.198	0.127	0.329
Column Total	0.037	0.312	0.217	0.566

Test statistic:

Chi square=0.566

yes

Chi square

df=(3-1)*(3-1)=4

c)

p-value=CHIDIST(0.566,4)=0.967

p-value > 0.100

d)Since the P-value > α, we fail to reject the null hypothesis.

e)

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