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 | 87 | 48 | 135 |

B | 90 | 55 | 145 |

C | 74 | 80 | 154 |

Column
Total |
251 | 183 | 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?

(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.)

(c) What are the degrees of freedom?

(d) Find or estimate the *P*-value of the sample test
statistic. (Round your answer to three decimal places.)

(e) 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.

Answer #1

The statistical software output for this problem is:

**Contingency table results:**

Rows: Ceremonial Ranking

Columns: None

Cooking Jar Sherds | Decorated Jar Sherds (Noncooking) | Total | |

A | 87 | 48 | 135 |

B | 90 | 55 | 145 |

C | 74 | 80 | 154 |

Total | 251 | 183 | 434 |

**Chi-Square test:**

Statistic |
DF |
Value |
P-value |
---|---|---|---|

Chi-square | 2 | 9.5282422 | 0.0085 |

Hence,

a) Level of significance = 0.05

b) Chi - square statistic = 9.528

c) Degrees of freedom = 2

d) P - value = 0.009

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

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
97
48
145
C
79
75
154
Column
Total
262
172
434
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