Question

The types of raw materials used to construct stone tools found at an archaeological site are...

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% 894
Obsidian 10.6% 165
Welded Tuff 11.4% 183
Pedernal chert 13.1% 199
Other 3.6% 45

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


(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 Student's t     chi-square normal uniform


What are the degrees of freedom?


(c) Find or estimate the P-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 the P-value > α, we fail to reject the null hypothesis. Since the P-value > α, we reject the null hypothesis.     Since the P-value ≤ α, we reject the null hypothesis. Since the P-value ≤ α, 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.    

Homework Answers

Answer #1

The following table is obtained:

Categories Observed Expected (fo-fe)2/fe
Category 1 894 1486*0.613=910.918 (894-910.918)2/910.918 = 0.314
Category 2 165 1486*0.106=157.516 (165-157.516)2/157.516 = 0.356
Category 3 183 1486*0.114=169.404 (183-169.404)2/169.404 = 1.091
Category 4 199 1486*0.131=194.666 (199-194.666)2/194.666 = 0.096
Category 5 45 1486*0.036=53.496 (45-53.496)2/53.496 = 1.349
Sum = 1486 1486 3.207

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