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% 912
Obsidian 10.6% 158
Welded Tuff 11.4% 173
Pedernal chert 13.1% 189
Other 3.6% 54

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 different.
H1: The distributions are the same.     H0: The distributions are the same.
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 chi-square     Student's t uniform normal


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

(a) level of significance = 0.01


the null and alternate hypotheses.

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

(b)

Raw Material Regional percent Oi Ei = 1486*pi (Oi - Ei)^2/Ei
Basalt 61.30% 912 910.918 0.0013
Obsidian 10.60% 158 157.516 0.0015
Welded tuff 11.40% 173 169.404 0.0763
pedernal chert 13.10% 189 194.666 0.1649
other 3.60% 54 53.496 0.0047
1486 0.2488

chi-square = 0.2488

All the expected frequencies greater than 5 (yes)


sampling distribution chi-square

df = 5 - 1 = 4

(c)
P-value > 0.10

(d)
Since the P-value > α, we fail to reject the null hypothesis.

(e)
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.   

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