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%	890
Obsidian	10.6%	162
Welded Tuff	11.4%	175
Pedernal chert	13.1%	212
Other	3.6%	47

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?

chi-square binomial     normal uniform Student's t

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	890	910.92	-0.69	0.480
2	0.106	162	157.52	0.36	0.128
3	0.114	175	169.40	0.43	0.185
4	0.131	212	194.67	1.24	1.544
5	0.036	47	53.50	-0.89	0.789
total	1.000	1486	1486		3.125

test statistic X² =3.125

Are all the expected frequencies greater than 5? :Yes

What sampling distribution will you use? :Chi square

degrees of freedom=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.