The types of raw materials used to construct stone tools found at an archaeological site are shown below. A random sample of 1486 stone tools were obtained from a current excavation site. Raw Material Basalt Obsidian Welded Tuff Pedernal chert Other USE SALT Regional Percent of Stone Tools 61.3% 10.6% 11.4% 13.1% 3.6% State the null and alternate hypotheses. O Ho: The distributions are the same. H₁: The distributions are different. O Ho: The distributions are different. H₁: The distributions are the same. O Ho: The distributions are different. H₁: The distributions are different. Use a 1% level of significance to test the claim that the regional distribution of raw materials fits the distribution at the current excavation site. (a) What is the level of significance? O Ho: The distributions are the same. H₁: The distributions are the same. No Observed Number of Tools as Current excavation Site Are all the expected frequencies greater than 5? Yes 900 160 166 216 44 (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.)
The types of raw materials used to construct stone tools found at an archaeological site are shown below. A random sample of 1486 stone tools were obtained from a current excavation site. Raw Material Basalt Obsidian Welded Tuff Pedernal chert Other USE SALT Regional Percent of Stone Tools 61.3% 10.6% 11.4% 13.1% 3.6% State the null and alternate hypotheses. O Ho: The distributions are the same. H₁: The distributions are different. O Ho: The distributions are different. H₁: The distributions are the same. O Ho: The distributions are different. H₁: The distributions are different. Use a 1% level of significance to test the claim that the regional distribution of raw materials fits the distribution at the current excavation site. (a) What is the level of significance? O Ho: The distributions are the same. H₁: The distributions are the same. No Observed Number of Tools as Current excavation Site Are all the expected frequencies greater than 5? Yes 900 160 166 216 44 (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.)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
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Question
100%
Transcribed Image Text:What sampling distribution will you use?
Obinomial
uniform
chi-square
Student's t
normal
What are the degrees of freedom?
(c) Find or estimate the P-value of the sample test statistic.
OP-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
OP-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 > a, we fail to reject the null hypothesis.
Since the P-value > a, we reject the null hypothesis.
O Since the P-value ≤ a, we reject the null hypothesis.
Since the P-value ≤ a, we fail to reject the null hypothesis.
(e) Interpret your conclusion in the context of the application.
O At the 0.01 level of significance, the evidence is sufficient to conclude that the regional distribution of raw
materials does not fit the distribution at the current excavation site.
At the 0.01 level of significance, the evidence is insufficient to conclude that the regional distribution of raw
materials does not fit the distribution at the current excavation site.
Transcribed Image Text:The types of raw materials used to construct stone tools found at an archaeological site are shown below. A random sample
of 1486 stone tools were obtained from a current excavation site.
Raw Material
Basalt
Obsidian
Welded Tuff
Pedernal chert
Other
USE SALT
Regional Percent
of Stone Tools
61.3%
10.6%
11.4%
13.1%
3.6%
State the null and alternate hypotheses.
O Ho: The distributions are the same.
H₁: The distributions are different.
O Ho: The distributions are different.
H₁: The distributions are the same.
O Ho: The distributions are different.
H₁: The distributions are different.
Use a 1% level of significance to test the claim that the regional distribution of raw materials fits the distribution at the
current excavation site.
(a) What is the level of significance?
O Ho: The distributions are the same.
H₁: The distributions are the same.
Observed Number of Tools
as Current excavation Site
900
160
166
216
44
Are all the expected frequencies greater than 5?
Yes
O No
(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.)
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