Question

In: Statistics and Probability

The types of raw materials used to construct stone tools found at an archaeological site are...

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% 903 Obsidian 10.6% 169 Welded Tuff 11.4% 169 Pedernal chert 13.1% 196 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 the same. H1: The distributions are the same. H0: The distributions are different. 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? Yes No What sampling distribution will you use? chi-square normal Student's t binomial uniform What are the degrees of freedom? (c) Find or estimate the P-value of the sample test statistic. P-value > 0.100 0.050 < P-value < 0.100 0.025 < P-value < 0.050 0.010 < P-value < 0.025 0.005 < P-value < 0.010 P-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

Solutions

Expert Solution

a) level of significance =0.01

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

b)

applying chi square goodness of fit test:
           relative observed Expected residual Chi square
category frequency(p) Oi Ei=total*p R2i=(Oi-Ei)/√Ei R2i=(Oi-Ei)2/Ei
1 0.6130 903.0000 910.92 -0.26 0.069
2 0.1060 169.0000 157.52 0.92 0.837
3 0.1140 169.0000 169.40 -0.03 0.001
4 0.1310 196.0000 194.67 0.10 0.009
5 0.0360 49.0000 53.50 -0.61 0.378
total 1.000 1486 1486 1.2941
test statistic X2 = 1.294
Are all the expected frequencies greater than 5? :Yes
What sampling distribution will you use? chi-square
degrees of freedom =categories-1=4

c)

P-value > 0.10

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


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