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 | 86 | 49 | 135 |

B | 89 | 56 | 145 |

C | 74 | 80 | 154 |

Column Total |
249 | 185 | 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.

*H*_{0}: Ceremonial ranking and pottery type are
not independent.

*H*_{1}: Ceremonial ranking and pottery type are
independent. *H*_{0}: Ceremonial ranking and pottery
type are independent.

*H*_{1}: Ceremonial ranking and pottery type are not
independent. *H*_{0}:
Ceremonial ranking and pottery type are not independent.

*H*_{1}: Ceremonial ranking and pottery type are not
independent. *H*_{0}: Ceremonial ranking and pottery
type are independent.

*H*_{1}: 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* binomial uniform
normal chi-square

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.

Answer #1

The statistical software output for this problem is:

Hence,

a) Level of significance = 0.05

Hypotheses: H0: Ceremonial ranking and pottery type are independent.

H1: Ceremonial ranking and pottery type are not independent.

b) Test statistic = 8.635

Yes

Chi - square

Degrees of freedom = 3

c) 0.010 < *p*-value < 0.025

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

e) At the 5% level of significance, there is sufficient evidence to conclude that ceremonial ranking and pottery type are not independent.

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 86 49 135 B 92 53 145 C 79 75 154
Column Total 257 177 434 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 434 sherds at an archaeological
location.
Ceremonial
Ranking
Cooking Jar
Sherds
Decorated
Jar Sherds (Noncooking)
Row
Total
A
90
45
135
B
94
51
145
C
78
76
154
Column
Total
262
172
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 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...

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
83
52
135
B
92
53
145
C
75
79
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...

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 85 50 135 B 95 50 145 C 79 75 154
Column Total 259 175 434 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 434 sherds at an archaeological
location.
Ceremonial Ranking
Cooking Jar Sherds
Decorated Jar Sherds (Noncooking)
Row Total
A
90
45
135
B
93
52
145
C
76
78
154
Column Total
259
175
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 434 sherds at an archaeological
location.
Ceremonial Ranking
Cooking Jar
Sherds
Decorated Jar Sherds
(Noncooking)
Row
Total
A
83
52
135
B
95
50
145
C
75
79
154
Column
Total
253
181
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 434 sherds at an archaeological
location.
Ceremonial
Ranking
Cooking Jar
Sherds
Decorated Jar Sherds
(Noncooking)
Row
Total
A
84
51
135
B
91
54
145
C
77
77
154
Column
Total
252
182
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 434 sherds at an archaeological
location.
Ceremonial Ranking
Cooking Jar
Sherds
Decorated Jar Sherds
(Noncooking)
Row
Total
A
82
53
135
B
95
50
145
C
77
77
154
Column
Total
254
180
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 434 sherds at an archaeological
location.
Ceremonial Ranking
Cooking Jar
Sherds
Decorated Jar Sherds
(Noncooking)
Row
Total
A
85
50
135
B
96
49
145
C
81
73
154
Column
Total
262
172
434
Use a chi-square test to determine if ceremonial ranking and
pottery type are independent at the 0.05 level of significance.
(a) Find the value of the chi-square statistic for the...

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