Ceremonial Ranking Decorated Jar Sherds (Noncooking) Row Total Cooking Jar Sherds 87 48 135 94 51 145 74 80 154 Column Total 255 179 434
The following table shows ceremonial ranking and type of pottery sherd for a random sample of 434 sherds at an archaeological location. Use a chi-square test to determine if ceremonial ranking and pottery type are independent at the 0.05 level of significance.
State the null and alternate hypotheses.
a) H0: Ceremonial ranking and pottery type are not independent.
H1: Ceremonial ranking and pottery type are not independent.
b) H0: Ceremonial ranking and pottery type are independent.
H1: Ceremonial ranking and pottery type are not independent.
c) H0: Ceremonial ranking and pottery type are independent.
H1: Ceremonial ranking and pottery type are independent.
d) H0: Ceremonial ranking and pottery type are not 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.)
What are the degrees of freedom?
Find or estimate the P-value of the sample test statistic. (Round your answer to three decimal places.)
(c) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis of independence?
b) Since the P-value > α, we reject the null hypothesis.
c) Since the P-value ≤ α, we reject the null hypothesis.
d) Since the P-value ≤ α, we fail to reject the null hypothesis.
b) 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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