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% 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

Answer 1

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