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 MaterialRegional Percent of Stone ToolsObserved Number of Tools as Current excavation SiteBasalt61.3%885Obsidian10.6%155Welded Tuff11.4%172Pedernal chert13.1%217Other3.6%57

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?

State the null and alternate hypotheses.

H₀: The distributions are different.

H₁: The distributions are different.

H₀: The distributions are the same.

H₁: The distributions are different.

H₀: The distributions are different.

H₁: The distributions are the same.

H₀: The distributions are the same.

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?

Yes

No

What sampling distribution will you use?

Student'st

binomial

normal

uniform

chi-square

What are the degrees of freedom?

(c) Find or estimate theP-value of the sample test statistic.

P-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

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?

Since theP-value >, we fail to reject the null hypothesis.

Since theP-value >, we reject the null hypothesis.

Since theP-value, we reject the null hypothesis.

Since theP-value, we fail to reject the null hypothesis.

(e) Interpret your conclusion in the context of the application.

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.