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%	900
Obsidian	10.6%	153
Welded Tuff	11.4%	165
Pedemal chert	13.1%	215
Other	3.6%	53

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 different.
H₁: The distributions are the same.    

H₀: The distributions are different.
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

normal     

chi-square

uniform

Student's t

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 > ?, we fail to reject the null hypothesis.

Since the P-value > ?, we reject the null hypothesis.    

Since the P-value ? ?, we reject the null hypothesis.

Since the P-value ? ?, 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

(a) What is the level of significance =0.01

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

b)

applying chi square goodness of fit test:

		observed	Expected		Chi square
category	Probability(p)	Oi	Ei=total*p		R2i=(Oi-Ei)2/Ei
Basalt	0.613	900.000	910.918		0.131
Obsidian	0.106	153.000	157.516		0.129
Welded Tuff	0.114	165.000	169.404		0.114
Pedemal chert	0.131	215.000	194.666		2.124
Other	0.036	53.000	53.496		0.005
total	1.000	1486	1486		2.503

chi square test statsiic =2.503

Are all the expected frequencies greater than 5--Yes

What sampling distribution will you use -chi square

degrees of freedom =categories-1=5-1=4

c)

estimate the P-value =0.644

d)

Since the P-value > ?, 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.