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 dferent excavation sites gave the information in the following table. Use a chi-square test with S% level of significance to test the claim that raw m for construction of stone tools and excavation site are independent. Stone Tool Construction Haterial Site A Material Site B Row Total Basat Obsidian 101 Peden cher Other Column Total 1315 195 1035 179 2724 768 547 94 499 536 91 1496 (a) What is the level of significance? State the null and alternate hypotheses O Hoi Stone tool material and site are independent. H Stone tool material and site are not independent. O Hai Stone tool material and site are not independent. H Stone tool material and site are independent O Hại Stone tool material and site are independent. H: Stone tool material and site are independent. O Ha! Stone tool material and site are not independent. H: 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 S? O Yes O No What sampling distribution will you use? O chi-square O normal O uniform O binomial O Student's What are the degrees of freedom? (e) Find or estimate the Pvalue of the sample test statistic. (Round your answer to three decimal places.) (4) Based on your answers in parts (a) to (e), will you reject or fail to reject the null hypothesis of independence? O Since the Pvalue>, we fail to reject the null hypothesis. O since the Pvaluea, we reject the nul hypothesis O since the Pvalue sa, we reject the null hypothesis.
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 dferent excavation sites gave the information in the following table. Use a chi-square test with S% level of significance to test the claim that raw m for construction of stone tools and excavation site are independent. Stone Tool Construction Haterial Site A Material Site B Row Total Basat Obsidian 101 Peden cher Other Column Total 1315 195 1035 179 2724 768 547 94 499 536 91 1496 (a) What is the level of significance? State the null and alternate hypotheses O Hoi Stone tool material and site are independent. H Stone tool material and site are not independent. O Hai Stone tool material and site are not independent. H Stone tool material and site are independent O Hại Stone tool material and site are independent. H: Stone tool material and site are independent. O Ha! Stone tool material and site are not independent. H: 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 S? O Yes O No What sampling distribution will you use? O chi-square O normal O uniform O binomial O Student's What are the degrees of freedom? (e) Find or estimate the Pvalue of the sample test statistic. (Round your answer to three decimal places.) (4) Based on your answers in parts (a) to (e), will you reject or fail to reject the null hypothesis of independence? O Since the Pvalue>, we fail to reject the null hypothesis. O since the Pvaluea, we reject the nul hypothesis O since the Pvalue sa, we reject the null hypothesis.
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
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Chapter10: Statistics
Section10.6: Summarizing Categorical Data
Problem 30PPS
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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 B
Row Total
Basalt
768
547
1315
Obsidian
101
94
195
Pedernal chert
Other
Column Total
536
499
1035
179
1496
1228
2724
(a) What is the level of significance?
State the null and alternate hypotheses.
O Ho: Stone tool material and site are independent.
H: 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 independent.
O Ho: Stone tool material and site are independent.
H: Stone tool material and site are independent.
O Ho: Stone tool material and site are not independent.
H: 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?
O Yes
O No
What sampling distribution will you use?
O chi-square
O normal
O uniform
O binomial
O Student'st
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?
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 s a, we reject the null hypothesis.
O Since the P-value s a, 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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