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. Stone Tool Construction Material Material Basalt Obsidian Pedernal chert Other Column Total Row Total 1315 195 Site A Site B 728 587 107 516 89 88 519 1035 90 179 1440 1284 2724 (a) What is the level of significance? State the null and alternate hypotheses. O Ho: Stone tool material and site are not independent. H: Stone tool material and site are independent. O Ho: Stone tool material and site are independent. H: Stone tool material and site are not independent. O Hạ: Stone tool material and site are not independent. H: Stone tool material and site are not independent. O Ho: Stone tool material and site are independent. H: Stone tool material and site 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? O Yes O No What sampling distribution will you use? O student's t O chi-square O normal O uniform O binomial

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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.

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.
Stone Tool Construction Material
Material
Site A
Site B
Row Total
Basalt
Obsidian
728
587
1315
107
88
195
Pedernal chert
516
519
1035
Other
Column Total
89
90
179
1440
1284
2724
(a) What is the level of significance?
State the null and alternate hypotheses.
O Hn: Stone tool material and site are not independent.
H,: Stone tool material and site are independent.
O Hn: Stone tool material and site are independent.
H1: Stone tool material and site are not independent.
O Ho: Stone tool material and site are not independent.
H: Stone tool material and site are not independent.
O Ho: Stone tool material and site are independent.
H1: Stone tool material and site 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?
O Yes
O No
What sampling distribution will you use?
O Student'st
O chi-square
O normal
O uniform
O binomial
Transcribed Image Text: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. Stone Tool Construction Material Material Site A Site B Row Total Basalt Obsidian 728 587 1315 107 88 195 Pedernal chert 516 519 1035 Other Column Total 89 90 179 1440 1284 2724 (a) What is the level of significance? State the null and alternate hypotheses. O Hn: Stone tool material and site are not independent. H,: Stone tool material and site are independent. O Hn: Stone tool material and site are independent. H1: Stone tool material and site are not independent. O Ho: Stone tool material and site are not independent. H: Stone tool material and site are not independent. O Ho: Stone tool material and site are independent. H1: Stone tool material and site 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? O Yes O No What sampling distribution will you use? O Student'st O chi-square O normal O uniform O 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.)
O p-value > 0.100
O 0.050 < p-value < 0.100
O 0.025 < p-value < 0.050
O 0.010 < p-value < 0.025
O 0.005 < p-value < 0.010
O 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?
O Since the P-value > a, we fail to reject the null hypothesis.
O Since the P-value > a, we reject the null hypothesis.
O since the P-value <a, we reject the null hypothesis.
O Since the P-value sa, we fail to reject the null hypothesis.
(e) Interpret your conclusion in the context of the application.
O At the 5% level of significance, there is sufficient evidence to conclude that stone tool construction material and site are not independent.
O At the 5% level of significance, there is insufficient evidence to conclude that stone tool construction material and site are not independent.
Transcribed Image Text: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.) O p-value > 0.100 O 0.050 < p-value < 0.100 O 0.025 < p-value < 0.050 O 0.010 < p-value < 0.025 O 0.005 < p-value < 0.010 O 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? O Since the P-value > a, we fail to reject the null hypothesis. O Since the P-value > a, we reject the null hypothesis. O since the P-value <a, we reject the null hypothesis. O Since the P-value sa, we fail to reject the null hypothesis. (e) Interpret your conclusion in the context of the application. O At the 5% level of significance, there is sufficient evidence to conclude that stone tool construction material and site are not independent. O At the 5% level of significance, there is insufficient evidence to conclude that stone tool construction material and site are not independent.
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