Question

In: Math

The following table shows ceremonial ranking and type of pottery sherd for a random sample of...

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 91 44 135
B 96 49 145
C 81 73 154
Column Total 268 166 434

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 not independent.
H1: Ceremonial ranking and pottery type are not independent.

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.


(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?

Student's t

uniform    

normal

chi-square

binomial


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 > α, we fail to reject the null hypothesis.

Since the P-value > α, we reject the null hypothesis.   

Since the P-value ≤ α, we reject the null hypothesis.

Since the P-value ≤ α, 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.    

Solutions

Expert Solution

ANSWER :

From the given data we have to determine the Ceremonial Ranking and Pottery type by using Chi- square test at a level of significance =0.05

H0  : Ceremonial ranking and pottery type are independent.
H1  : Ceremonial ranking and pottery type are not independent.

(b) Applying Chi- square test

Expected Ei = row total x column total / grand total Cooking Decorated Total
A 135*268 / 434 = 83.36 135*166 / 434 = 51.635 135
B 145*268 /434 = 89.539 145*166 / 434 = 55.46 145
C 154*268 / 434 = 95.096

154*166 / 434 = 58.90

154
Total 268 166 434
  
Chi square X2

= ( Oi - Ei )2 / Ei

where Oi = observed Frequency

Ei = expected Frequency

Cooking Decorated Total
A 0.7002 1.1257 1.8259
B 0.4662 0.7524 1.2186
C 2.0894 3.3753 5.4647
TOTAL 3.2558 5.2534 8.5092

Chi - Square statistic for the sample = 8.5092

Expected Frequencies are Greater than 5 : Yes


What sampling distribution will you use?  

answer : I will choose Chi square

Degrees Of Freedom = ( rows-1)* ( columns -1) = (3-1)*(2-1) = 2

(C)

0.05 < p- value < 0.010

Here the sample test statistic value is 8.5092 So at the level of significance where p value it is less than 0.010.

(D) From the above where p - value is very less it can be ignored

Since the P-value ≤ α, we reject the null hypothesis.

(E)

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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The following table shows ceremonial ranking and type of pottery sherd for a random sample of...
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 89 46 135 B 95 50 145 C 81 73 154 Column Total 265 169 434 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...
The following table shows ceremonial ranking and type of pottery sherd for a random sample of...
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The following table shows ceremonial ranking and type of pottery sherd for a random sample of...
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 91 44 135 B 94 51 145 C 80 74 154 Column Total 265 169 434 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...
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