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%	910
Obsidian	10.6%	161
Welded Tuff	11.4%	173
Pedernal chert	13.1%	185
Other	3.6%	57

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 the same.H₀: The distributions are different.
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?

YesNo    

What sampling distribution will you use?

Student's tchi-square    uniformnormalbinomial

What are the degrees of freedom?


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

P-value > 0.1000.050 < P-value < 0.100    0.025 < P-value < 0.0500.010 < P-value < 0.0250.005 < P-value < 0.010P-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 alternative hypothesis is

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

b)

Test statistic is

O: Observed frequency
E: Expected frequency.

E = n*pi

n = 1486

	O	p	E	(O-E)	(O-E)^2	(O-E)^2/E
	910	0.613	910.918	-0.918	0.842724	0.000925
	161	0.106	157.516	3.484	12.13826	0.07706
	173	0.114	169.404	3.596	12.93122	0.076334
	185	0.131	194.666	-9.666	93.43156	0.479958
	57	0.036	53.496	3.504	12.27802	0.229513
Total	1486					0.864

Yes, all the expected frequencies greater than 5.

The sampling distribution we use chi-square.

Degrees of freedom = Number of E's - 1 = 5 - 1 = 4

c)

0.90 < P-value < 0.95

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.