served Number of Tools as Current excavation Site Basalt 61.3% 902 Obsidian 10.6% 165 Welded Tuff 11.4% 166 Pedernal chert 13.1% 204 Other 3.6% 49 Use a 1% level of significance to test the claim that the regional
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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 | Regional Percent of Stone Tools | Observed Number of Tools as Current excavation Site |
| Basalt | 61.3% | 902 |
| Obsidian | 10.6% | 165 |
| Welded Tuff | 11.4% | 166 |
| Pedernal chert | 13.1% | 204 |
| Other | 3.6% | 49 |
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.
State the null and alternate hypotheses.
H1: The distributions are the same.H0: The distributions are the same.
H1: The distributions are different. H0: The distributions are different.
H1: The distributions are different.H0: The distributions are different.
H1: The distributions are the same.
(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?
What sampling distribution will you use?
What are the degrees of freedom?
(c) Find or estimate the P-value of the sample test statistic.
(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis of independence?
(e) Interpret your conclusion in the context of the application.
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Here the types of raw materials used to construct stone tools found at an archaeological site are shown below.
| Raw Material | Regional Percent of Stone Tools | Observed Number of Tools as Current excavation Site | |
| Basalt | 61.30% | 902 | |
| Obsidian | 10.60% | 165 | |
| Welded Tuff | 11.40% | 166 | |
| Pedernal chert | 13.10% | 204 | |
| Other | 3.60% | 49 |
It is required to test the claim that the regional distribution of raw materials fits the distribution at the current excavation site.
The given level of significance is α =0.01.
To test the above claim the most appropriate test is the chi-square goodness of fit test.
The null and alternative hypothesis are
H0: The distributions are the same.
H1: The distributions are different.
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