The following table shows site type and type of pottery for a random sample of 628 sherds at an archaeological location. Pottery Type McElmo Black-on-White 59 68 Site Type Mesa Top Cliff-Talus Canyon Bench Column Total USE SALT Mesa Verde Black-on-White 80 81 91 252 72 199 Mancos Black-on-White 50 64 63 177 Row Total 189 213 226 628 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?

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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
McElmo
Black-on-White
59
68
72
199
Site Type
Mesa Top
Cliff-Talus
Canyon Bench
Column Total
USE SALT
Mesa Verde
Black-on-White
80
81
91
252
State the null and alternate hypotheses.
O Ho: Site type and pottery are independent.
H₁: Site type and pottery are independent.
O Ho: Site type and pottery are not independent.
H₁: Site type and pottery are not independent.
O Ho: Site type and pottery are independent.
H₁: Site type and pottery are not independent.
O Ho: Site type and pottery are not independent.
H₁: Site type and pottery are independent.
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?
Mancos
Black-on-White
50
Are all the expected frequencies greater than 5?
O Yes
O No
64
63
177
What sampling distribution will you use?
O Student's t
O chi-square
O normal
O binomial
O uniform
Row Total
189
213
226
628
(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.)
Transcribed Image Text:The following table shows site type and type of pottery for a random sample of 628 sherds at an archaeological location. Pottery Type McElmo Black-on-White 59 68 72 199 Site Type Mesa Top Cliff-Talus Canyon Bench Column Total USE SALT Mesa Verde Black-on-White 80 81 91 252 State the null and alternate hypotheses. O Ho: Site type and pottery are independent. H₁: Site type and pottery are independent. O Ho: Site type and pottery are not independent. H₁: Site type and pottery are not independent. O Ho: Site type and pottery are independent. H₁: Site type and pottery are not independent. O Ho: Site type and pottery are not independent. H₁: Site type and pottery are independent. 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? Mancos Black-on-White 50 Are all the expected frequencies greater than 5? O Yes O No 64 63 177 What sampling distribution will you use? O Student's t O chi-square O normal O binomial O uniform Row Total 189 213 226 628 (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.)
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
0.025 < p-value < 0.050
O 0.010 < p-value < 0.025
O 0.005 < p-value < 0.010
O 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-value ≤ a, we reject the null hypothesis.
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.
At the 1% level of significance, there is insufficient evidence to conclude that site and pottery type are not independent.
Transcribed Image Text: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 0.025 < p-value < 0.050 O 0.010 < p-value < 0.025 O 0.005 < p-value < 0.010 O 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-value ≤ a, we reject the null hypothesis. 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. At the 1% level of significance, there is insufficient evidence to conclude that site and pottery type are not independent.
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Hi there, what should I select for the second part of (a) ? And whic hdo I select for the value of the chi-square statistic for the sample, letter (b)?

Thank you for your help, I really appreciate it!

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