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.

Raw Material	Regional Percent of Stone Tools	Observed Number of Tools as Current excavation Site
Basalt	61.3%	925
Obsidian	10.6%	154
Welded Tuff	11.4%	174
Pedernal chert	13.1%	189
Other	3.6%	44

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 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.

(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's t

binomial    

uniform

normal

chi-square

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.    

Answer 1

a) level of significance =0.01

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

b)

applying chi square tesT:

	relative	observed	Expected	residual	Chi square
category	frequency	Oi	Ei=total*p	R2i=(Oi-Ei)/√Ei	R2i=(Oi-Ei)2/Ei
1	0.613	925	910.92	0.47	0.218
2	0.106	154	157.52	-0.28	0.078
3	0.114	174	169.40	0.35	0.125
4	0.131	189	194.67	-0.41	0.165
5	0.036	44	53.50	-1.30	1.686
total	1.000	1486	1486		2.271

value of the chi-square statistic =2.271

Are all the expected frequencies greater than 5? :Yes

What sampling distribution will you use? Chi square

degree of freedom =categories-1=

4

c) P-value > 0.100

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.