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%	898
Obsidian	10.6%	163
Welded Tuff	11.4%	165
Pedernal chert	13.1%	197
Other	3.6%	63

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) 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.)
=

Answer 1

Solution:

Given:

Claim:  the regional distribution of raw materials fits the distribution at the current excavation site.

Thus hypothesis are:

H0: the regional distribution of raw materials fits the distribution at the current excavation site.

H₀: The distributions are the same.
Vs

H1: the regional distribution of raw materials does NOT fit the distribution at the current excavation site.

H₁: The distributions are different.

Level of significance = 0.01

Part a) Find the value of the chi-square statistic for the sample

Chi square test statistic for goodness of fit

Where

O_i = Observed Counts

E_i =Expected Counts = N * Regional Percent of Stone Tools

Thus we need to make following table:

Raw Material	Regional Percent of Stone Tools	Oi: Observed Number of Tools as Current excavation Site	Ei: Expected frequencies	Oi^2/Ei
Basalt	61.30%	898	910.918	885.265
Obsidian	10.60%	163	157.516	168.675
Welded Tuff	11.40%	165	169.404	160.710
Pedernal chert	13.10%	197	194.666	199.362
Other	3.60%	63	53.496	74.192
		N = 1486

Thus

Are all the expected frequencies greater than 5?

Yes

Sampling distribution:

Chi-square

the degrees of freedom

df = k - 1 = 5 -1 = 4

Part c) estimate the P-value

Use following Excel command:

=CHISQ.DIST.RT(2.205,4)

=0.698

P-value = 0.698

Part d) will you reject or fail to reject the null hypothesis of independence?

Since P-value = 0.698 > 0.01 level of significance, we fail to reject H0.

Since the P-value > α, we fail to reject the null hypothesis

Part e) Interpret your conclusion in the context of the application.

At the 0.01 level of significance, there is insufficient evidence to conclude that the regional distribution of raw materials and the current excavation site distribution are not independent.