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 Black-on-White 77 McElmo Black-on-White Row Total Mancos Black-on-White 51 61 189 Mesa Top Cliff-Talus Canyon Bench 80 67 66 213 87 71 68 226 Column Total 244 199 185 628 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. OH: Site type and pottery are independent. H₁: Site type and pottery are not independent. OH: Site type and pottery are not independent. H₁: Site type and pottery are independent. OH: Site type and pottery are independent. H₁: Site type and pottery are independent. OH: Site type and pottery are not independent. H₁: 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 O No What sampling distribution will you use? O uniform O chi-square O Student's t O binomial normal 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 ○ 0.050 < p-value < 0.100 O 0.025 a, we fail to reject the null hypothesis. O Since the P-value > a, we reject the null hypothesis. O Since the P-value sa, we reject the null hypothesis. O Since the P-value ≤ a, we fail to reject the null hypothesis. (e) Interpret your conclusion in the context of the application. O At the 1% level of significance, there is sufficient evidence to conclude that site and pottery type are not independent. O At the 1% level of significance, there is insufficient evidence to conclude that site and pottery type are not independent.