he following table shows site type and type of pottery for a random sample of 628 sherds at an archaeological location. Pottery Type Site Type Mesa Verde Black-on-White McElmo Black-on-White Mancos Black-on-White Row Total Mesa Top 80 56 53 189 Cliff-Talus 84 72 57 213 Canyon Bench 91 72 63 226 Column Total 255 200 173 628 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? State the null and alternate hypotheses. H0: Site type and pottery are not independent. H1: Site type and pottery are independent.H0: Site type and pottery are not independent. H1: Site type and pottery are not independent. H0: Site type and pottery are independent. H1: Site type and pottery are not independent.H0: Site type and pottery are 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? uniform binomial chi-square Student'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 < 0.010 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 > ?, 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.

he following table shows site type and type of pottery for a random sample of 628 sherds at an archaeological location. Pottery Type Site Type Mesa Verde Black-on-White McElmo Black-on-White Mancos Black-on-White Row Total Mesa Top 80 56 53 189 Cliff-Talus 84 72 57 213 Canyon Bench 91 72 63 226 Column Total 255 200 173 628 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? State the null and alternate hypotheses. H0: Site type and pottery are not independent. H1: Site type and pottery are independent.H0: Site type and pottery are not independent. H1: Site type and pottery are not independent. H0: Site type and pottery are independent. H1: Site type and pottery are not independent.H0: Site type and pottery are 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? uniform binomial chi-square Student'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 < 0.010 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 > ?, 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.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

The following table shows site type and type of pottery for a random sample of 628 sherds at an archaeological location.

	Pottery Type
Site Type	Mesa Verde Black-on-White	McElmo Black-on-White	Mancos Black-on-White	Row Total
Mesa Top	80	56	53	189
Cliff-Talus	84	72	57	213
Canyon Bench	91	72	63	226
Column Total	255	200	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?

State the null and alternate hypotheses.

H₀: Site type and pottery are not independent.
H₁: Site type and pottery are independent.H₀: Site type and pottery are not independent.
H₁: Site type and pottery are not independent. H₀: Site type and pottery are independent.
H₁: Site type and pottery are not independent.H₀: Site type and pottery are 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?

uniform

binomial

chi-square

Student'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 < 0.010

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 > ?, 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.

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