The Focus Problem at the beginning of the chapter refers to excavations at Burnt Mesa Pueblo in Bandelier National Monument. One question the archaeologists asked was: Is the raw material used by prehistoric Indians for stone tool manufacture independent of the archaeological excavation site? Two different excavation sites at Burnt Mesa Pueblo gave the information in the following table. Use a chi-square test with 5% level of significance to test the claim that the raw material used for construction of stone tools and the excavation site are independent.

Please provide the following information:
(a) What is the level of significance? State the null and alternate hypotheses.
(b) Find the value of the chi-square statistic for the sample. Are all the expected frequencies greater than 5? What sampling distribution will you use? What are the degrees of freedom?
(c) Find or estimate the P-value of the sample test statistic.
(d) Based on your answers in parts (a)€“(c), will you reject or fail to reject the null hypothesis of independence?
(e) Your conclusion in the context of the application.
Use the expected values E to the hundredths place.

Stone Tool Construction Material, Burnt Mesa Pueblo Material Basalt Obsidian Pedernal chert Other Column Total Site A 731 102 510 85 1428 Site B 584 93 525 94 1296 Row Total 1315 195 1035 179 2724