The following table shows ceremonial ranking and type of pottery sherd for a random sample of 434 sherds at an archaeological location. Ceremonial Ranking Cooking Jar Sherds Decorated Jar Sherds (Noncooking) Row Total A 81 54 135 B 95 50 145 C 74 80 154 Column Total 250 184 434 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 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 not 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? chi-squarebinomial uniformStudent's tnormal 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 > 0.1000.050 < P-value < 0.100 0.025 < P-value < 0.0500.010 < P-value < 0.0250.005 < P-value < 0.010P-value < 0.005
The following table shows ceremonial ranking and type of pottery sherd for a random sample of 434 sherds at an archaeological location. Ceremonial Ranking Cooking Jar Sherds Decorated Jar Sherds (Noncooking) Row Total A 81 54 135 B 95 50 145 C 74 80 154 Column Total 250 184 434 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 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 not 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? chi-squarebinomial uniformStudent's tnormal 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 > 0.1000.050 < P-value < 0.100 0.025 < P-value < 0.0500.010 < P-value < 0.0250.005 < P-value < 0.010P-value < 0.005
Holt Mcdougal Larson Pre-algebra: Student Edition 2012
1st Edition
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Chapter11: Data Analysis And Probability
Section: Chapter Questions
Problem 8CR
Related questions
Question
The following table shows ceremonial ranking and type of pottery sherd for a random sample of 434 sherds at an archaeological location.
Ceremonial Ranking | Cooking Jar Sherds | Decorated Jar Sherds (Noncooking) |
Row Total |
---|---|---|---|
A | 81 | 54 | 135 |
B | 95 | 50 | 145 |
C | 74 | 80 | 154 |
Column Total | 250 | 184 | 434 |
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 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 not 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?
chi-squarebinomial uniformStudent's tnormal
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 > 0.1000.050 < P-value < 0.100 0.025 < P-value < 0.0500.010 < P-value < 0.0250.005 < P-value < 0.010P-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 > ?, 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.
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