The types of raw materials used to construct stone tools found at an archaeologi

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.

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.

What sampling distribution will you use?

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

Raw Material Regional Percent of Stone Tools Observed Number of Tools as Current excavation Site Basalt 61.3% 919 Obsidian 10.6% 156 Welded Tuff 11.4% 181 Pedemal chert 13.1% 185 Other 3.6% 45

Explanation / Answer

Answer:

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.

(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.)
  2.709

Are all the expected frequencies greater than 5?

Yes  

What sampling distribution will you use?

chi-square    
What are the degrees of freedom?
  df=4

(c) Find or estimate the P-value of the sample test statistic. (Round your answer to three decimal places.)
  P=0.608

(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.

.

(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.    

Goodness of Fit Test

observed

expected

O - E

(O - E)² / E

919

910.918

8.082

0.072

156

157.516

-1.516

0.015

181

169.404

11.596

0.794

185

194.666

-9.666

0.480

45

53.496

-8.496

1.349

Total

1486

1486.000

2.709

2.71

chi-square

4

df

.6076

p-value

Goodness of Fit Test

observed

expected

O - E

(O - E)² / E

919

910.918

8.082

0.072

156

157.516

-1.516

0.015

181

169.404

11.596

0.794

185

194.666

-9.666

0.480

45

53.496

-8.496

1.349

Total

1486

1486.000

2.709

2.71

chi-square

4

df

.6076

p-value

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