Question

The following table shows site type and type of pottery for a random sample of 628 sherds at an archaeological location. Pottery Type Mesa Verde McElmo Mancos Site Type Black White Black-on-White Row Total Black-on-White | Mesa Top 77T 189 Cliff-Talus 81 213 Canyon Bench 226 Column Total 248 207 173 628 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? - 61 90 State the null and alternate hypotheses. Ho: Site type and pottery are not independent. H: Site type and pottery are not independent. Ho: Site type and pottery are independent. H: Site type and pottery are independent. Ho: Site type and pottery are independent. H: Site type and pottery are not independent. Ho Site type and pottery are not independent. H: 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? chi-square binomial uniform Student'st 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.) p-value > 0.100 0.050 < p-value < 0.100 0.025 < p-value < 0.050 0.010 < p-value < 0.025 0.005 < p-value < 0.010 p-value < 0.005 (d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis of independence? Since the p-value > a, we fail to reject the null hypothesis. Since the p-value > a, we reject the null hypothesis. Since the p-values a, we reject the null hypothesis. Since the p-values a, we fail to reject the null hypothesis. (e) Interpret your conclusion in the context of the application. At the 1% level of significance, there is sufficient evidence to conclude that site and pottery type are not independent. At the 1% level of significance, there is insufficient evidence to conclude that site and pottery type are not independent.

Answer 1

a) level of significance =0.05

Ho Site type and pottery are independent. H: Site type and pottery are not independent.

b)

Applying chi square test of independence:

Expected	Ei=row total*column total/grand total	Mesa verde	McElmo	Mancos	Total
	Mesa Top	74.64	62.30	52.07	189
	Cliff Talus	84.11	70.21	58.68	213
	Canyon Bench	89.25	74.49	62.26	226
	total	248	207	173	628
chi square    χ2	=(Oi-Ei)2/Ei	Mesa verde	McElmo	Mancos	Total
	Mesa Top	0.075	0.008	0.180	0.2632
	Cliff Talus	0.115	0.009	0.092	0.2162
	Canyon Bench	0.006	0.030	0.009	0.0451
	total	0.1965	0.0468	0.2813	0.5246
test statistic X2 =		0.525

Yes

What sampling distribution will you use? chi-square

degrees of freedom =(row-1)*(column-1)=4

p-value > 0.100

d)

Since the P-value > a, we fail to reject the null hypothesis.

e)

At the 1% level of significance, there is insufficient evidence to conclude that site and pottery type are not independent.