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%	163
Welded Tuff	11.4%	176
Pedemal chert	13.1%	186
Other	3.6%	49

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 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?

YesNo    

What sampling distribution will you use?

Student's tbinomial    chi-squarenormaluniform

What are the degrees of freedom?


(c) Find or estimate the P-value of the sample test statistic. (Round your answer to three decimal places.)


(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, there is sufficient evidence to conclude that the regional distribution of raw materials and the current excavation site distribution are not independent.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.    

Answer 1

The statistical software output for this problem is:

Hence,

a) Level of significance = 0.01

Hypotheses:

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

b) Test statistic = 1.213

Yes

Chi - Square

Degrees of freedom = 4

c) P - value = 0.876

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

e) 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.