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%	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.    

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.