This question refers to excavations at a national monument. One question the arc

Question

This question refers to excavations at a national monument. One question the archaeologists asked was: Is raw material used by prehistoric Indians for stone tool manufacture independent of the archaeological excavation site? Two different excavation sites gave the information in the following table. Use a chi-square test with 5% level of significance to test the claim that raw material used for construction of stone tools and excavation site are independent.

(a) What is the level of significance?


State the null and alternate hypotheses.

H0: Stone tool material and site are independent.
H1: Stone tool material and site are independent.H0: Stone tool material and site are not independent.
H1: Stone tool material and site are not independent.    H0: Stone tool material and site are not independent.
H1: Stone tool material and site are independent.H0: Stone tool material and site are independent.
H1: Stone tool material and site 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?

YesNo    

What sampling distribution will you use?

chi-squarebinomial    uniformStudent's tnormal

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 5% level of significance, there is sufficient evidence to conclude that stone tool construction material and site are not independent.At the 5% level of significance, there is insufficient evidence to conclude that stone tool construction material and site are not independent.    

Stone Tool Construction Material Material Site A Site B Row Total Basalt 738 577 1315 Obsidian 101 94 195 Pedernal chert 494 541 1035 Other 76 103 179 Column Total 1409 1315 2724

Explanation / Answer

a) Level of significance = 0.05

Null and alternative hypotheses:

H0: Stone tool material and site are independent.
H1: Stone tool material and site are not independent.

Statistical software output for this problem is:

Contingency table results:
Rows: Material
Columns: None

Chi-Square test:

Hence,

b) Test statistic = 22.954

Yes

Chi Square

Degrees of freedom = 3

c) P - value = 0.000

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

e) At the 5% level of significance, there is sufficient evidence to conclude that stone tool construction material and site are not independent.

Site A Site B Total Basalt 738 577 1315 Obsidian 101 94 195 Pedernal chert 494 541 1035 Other 76 103 179 Total 1409 1315 2724

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