Question

The following table shows site type and type of pottery for a random sample of 628 sherds at an archaeological location. 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 Ho: Site type and pottery are not independent. Hy: Site type and pottery are not independent. Ho: Site type and pottery are independent. Hy: Site type and pottery are independent. Ho: Site type and pottery are independent. Hi: Site type and pottery are not independent. Ho: Site type and pottery are not independent. Hi: Site type and pottery are 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? Yes No What sampling distribution will you use? Student'st normal chi-square binomial uniform 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.) (d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis of independence?

Answer 1

# 9 n=620 clevel of segnificance)=0.01 ise = 10% Hypothesis is, in Ho! site type and pottery type are not independent His site type and pottery type are independent. so option @ is correct ery y Expected frequency = Row sum x column Sum Grand Total Expected frequency teable Ma cos Site teppe mese verde 189x179 - 53.877 Mesa ! 189 x 252 - 75.24 Top 10 9 x197 =59.200 620 620 Clift-Tulus 213 x 252 = 05.471 213x197 - 66.817 213X 179 - 60:712 Can youn Bench 226X252 = 60.618 226X197 = 70.095 226 x 119 = 64.417 type • Mectino 620 620 628 620 628 (0;-E;)? Observed 10.) EL Expected (21) 75.841 59.200 79 9.979 0.507 14.985 so 79 53.871 85.47) .66.817 Go.712 go.680 70.895 64.417 41.874 30. 229 0.083 10.969 47.541 12.038 94 64 177.005 Total X = { coi-Eid = 1177.005

Yows yes All expected frequencies greater than s. We use chi-square sampling distribution. • Degree of freedom = (8-1) (C-1). = (3-1)(3-1) → Colums. = 2x2 =4 c) 13.277 Critical value (22 de 0.01, and p-value at you (from p-valine table (0.01, 4) = 3 114 x 37 of chi-square] online calculatora | d) Here p-value to <0.05, we Reject Null hypothesis option ® is correct. lie. Since p-value < x=0.01 , we reject null Hypothesis. e) option is correct. At the 1% level of segnificance, there is insufficient evidence to conclude that site type and pottery type are not independent." Please give up rate if it is helpul to you