1. 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. Raw Material Regional Percent of Observed Number of Tools as Stone Tools Current excavation Site Basalt 61.3% 915 Obsidian 10.6% 152 Welded Tuff 11.4% 173 Pedernal chert 13.1% 190 Other 3.6% 56 (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. Benford's Law states that the first nonzero digits of numbers drawn at random from a large complex data file have the following probability distribution. t First Nonzero Digit 1 2 4 5 6 7 8 9 Probability 0.301 0.176 0.125 0.097 0.079 0.067 0.058 0.051 0.046 Suppose that n = 275 numerical entries were drawn at random from a large accounting file of a major corporation. The first nonzero digits were recorded for the sample. First Nonzero Digit 1 2 3 4 5 6 7 8 9 Sample Frequency 83 49 33 22 24 18 13 17 16 Use a 1% level of significance to test the claim that the distribution of first nonzero digits in this accounting file follows Benford's Law. (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.)