The following table shows site type and type of pottery for a random sample of 6
ID: 3235811 • Letter: T
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.
H0: Site type and pottery are independent.
H1: Site type and pottery are independent.H0: Site type and pottery are independent.
H1: Site type and pottery are not independent. H0: Site type and pottery are not independent.
H1: Site type and pottery are not independent.H0: Site type and pottery are not independent.
H1: 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?
YesNo
What sampling distribution will you use?
normaluniform Student's tchi-squarebinomial
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?
Since the P-value > , we fail to reject the null hypothesis.Since the P-value > , we reject the null hypothesis. Since the P-value , we reject the null hypothesis.Since the P-value , 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.
8.–/9 pointsBBUnderStat10 10.1.012.My Notes
The following table shows ceremonial ranking and type of pottery sherd for a random sample of 434 sherds at an archaeological location.
Use a chi-square test to determine if ceremonial ranking and pottery type are independent at the 0.05 level of significance.(a) What is the level of significance?
State the null and alternate hypotheses.
H0: Ceremonial ranking and pottery type are not independent.
H1: Ceremonial ranking and pottery type are not independent.H0: Ceremonial ranking and pottery type are not independent.
H1: Ceremonial ranking and pottery type are independent. H0: Ceremonial ranking and pottery type are independent.
H1: Ceremonial ranking and pottery type are independent.H0: Ceremonial ranking and pottery type are independent.
H1: Ceremonial ranking and pottery type 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?
YesNo
What sampling distribution will you use?
Student's tchi-square uniformbinomialnormal
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?
Since the P-value > , we fail to reject the null hypothesis.Since the P-value > , we reject the null hypothesis. Since the P-value , we reject the null hypothesis.Since the P-value , we fail to reject the null hypothesis.
(e) Interpret your conclusion in the context of the application.
At the 5% level of significance, there is sufficient evidence to conclude that ceremonial ranking and pottery type are not independent.At the 5% level of significance, there is insufficient evidence to conclude that ceremonial ranking and pottery type are not independent.
Pottery Type Site Type Mesa VerdeBlack-on-White McElmo
Black-on-White Mancos
Black-on-White Row Total Mesa Top 75 63 51 189 Cliff-Talus 80 66 67 213 Canyon Bench 93 66 67 226 Column Total 248 195 185 628 Need Help?
Explanation / Answer
(a) What is the level of significance? Ans: 0.01
State the null and alternate hypotheses.
H0: Site type and pottery are independent.
H1: Site type and pottery are not independent
Are all the expected frequencies greater than 5?
No
What sampling distribution will you use?
Chi Square test
What are the degrees of freedom?
(r-1)*(c-1) = (3-1)*(3-1) = 2*2 = 4
(c) Find or estimate the P-value of the sample test statistic. (Round your answer to three decimal places.)
Answer: 0.736
(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 > , 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 insufficient evidence to conclude that site and pottery type are not independent.
Pottery Type Expected Freq Site Type Mesa Verde McElmo Mancos Row Total Mesa Verde McElmo Mancos Row Total Black-on-White Black-on-White Black-on-White Black-on-White Black-on-White Black-on-White Mesa Top 75 63 51 189 74.637 58.686 55.677 189.000 Cliff-Talus 80 66 67 213 84.115 66.139 62.747 213.000 Canyon Bench 93 66 67 226 89.248 70.175 66.576 226.000 Column Total 248 195 185 628 248.000 195.000 185.000 628.000Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.