The types of raw materials used to construct stone tools foundat an archaeological site are shown below. A random sample of 1486stone tools were obtained from a current excavation site.

Raw Material	Regional Percent of Stone Tools	Observed Number of Tools as Current excavationSite
Basalt	61.3%	905
Obsidian	10.6%	163
Welded Tuff	11.4%	165
Pedernal chert	13.1%	201
Other	3.6%	52

Use a 1% level of significance to test the claim that theregional distribution of raw materials fits the distribution at thecurrent 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 the same.
H₁: The distributions aredifferent.    

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?

Yes

No    

What sampling distribution will you use?

normal

Student's t    

binomial

uniform

chi-square

What are the degrees of freedom?


(c) Find or estimate the P-value of the sample teststatistic.

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 orfail to reject the null hypothesis of independence?

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

Since the P-value > ?, we reject the nullhypothesis.    

Since the P-value ? ?, we reject the nullhypothesis.

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

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

At the 0.01 level of significance, the evidence is sufficient toconclude that the regional distribution of raw materials does notfit the distribution at the current excavation site.

At the 0.01 level of significance, the evidence is insufficientto conclude that the regional distribution of raw materials doesnot fit the distribution at the current excavation site.