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The following table shows site type and type of pottery for a random sample of 628 sherds at an archaeological location. Pottery Type Site Type Mesa Verde McElmo Mancos Row Total Black on-White Black on-White Black-on-White Mesa Top 72 55 62 189 Cliff-Talus 82 67 64 213 Canyon Bench 89 63 74 226 Column Total 243 185 200 628 LA USE SALT Use a chi-square test to determine if site type and pottery type are independent at the 0.01 level of significance. a) What is the level of significance? State the null and alternate hypotheses. O Ho: Site type and pottery are not independent. H, : Site type and pottery are not independent. O Ho: Site type and pottery are not independent. H, : Site type and pottery are independent. OH: Site type and pottery are independent. H, : Site type and pottery are independent. O Ho: Site type and pottery are independent. H : Site type and pottery are not independent. (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? O Yes No What sampling distribution will you use? O chi-square O uniform O binomial O normal O Student's t What are the degrees of freedom? (c) Find or estimate the P-value of the sample test statistic. (Round your answer to three decimal places.) O p-value > 0.100 O 0.050 a, we fail to reject the null hypothesis. Since the P-value > a, we reject the null hypothesis. Since the P-value S a, we reject the null hypothesis. Since the P-value S a, we fail to reject the null hypothesis. (e) Interpret your conclusion in the context of the application. O At the 1% level of signif O At the 1% level of significance, there is insufficient evidence to conclude that site and pottery type are not independent