The types of raw materials used to construct stone tools found at an archaeologi

Question

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.

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 the same.
H1: The distributions are different.H0:

The distributions are different.
H1: The distributions are the same.    

H0: The distributions are different.
H1: The distributions are different.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?

binomial

normal     

chi-square

uniform

Student's t

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?

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

Since the P-value > ?, we reject the null hypothesis.    

Since the P-value ? ?, we reject the null hypothesis.

Since the P-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, there is sufficient evidence to conclude that the regional distribution of raw materials and the current excavation site distribution are not independent.

At the 0.01 level of significance, there is insufficient evidence to conclude that the regional distribution of raw materials and the current excavation site distribution are not independent.

Raw Material Regional Percent of Stone Tools Observed Number of Tools as Current excavation Site Basalt 61.3% 900 Obsidian 10.6% 153 Welded Tuff 11.4% 165 Pedemal chert 13.1% 215 Other 3.6% 53

Explanation / Answer

(a) What is the level of significance =0.01

H0: The distributions are the same.
H1: The distributions are different.

b)

applying chi square goodness of fit test:

chi square test statsiic =2.503

Are all the expected frequencies greater than 5--Yes

What sampling distribution will you use -chi square

degrees of freedom =categories-1=5-1=4

c)

estimate the P-value =0.644

d)

Since the P-value > ?, we fail to reject the null hypothesis

e)

At the 0.01 level of significance, there is insufficient evidence to conclude that the regional distribution of raw materials and the current excavation site distribution are not independent.

observed Expected Chi square category Probability(p) Oi Ei=total*p R2i=(Oi-Ei)2/Ei Basalt 0.613 900.000 910.918 0.131 Obsidian 0.106 153.000 157.516 0.129 Welded Tuff 0.114 165.000 169.404 0.114 Pedemal chert 0.131 215.000 194.666 2.124 Other 0.036 53.000 53.496 0.005 total 1.000 1486 1486 2.503

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