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

Pottery Type

Site Type Mesa VerdeBlack-on-White McElmoBlack-on-White MancosBlack-on-White Row Total

mesa top 77 57 55 189

cliff-talus 79 66 68 213

canyon bench 88 66 72 226

column total 244 189 195 628

Use a chi-square test to determine if site and pottery are independent at the 0.01 level of significance.

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.)

Find or estimate theP-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

Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis of independence?

Since theP-value >, we fail to reject the null hypothesis.

Since theP-value >, we reject the null hypothesis.

Since theP-value, we reject the null hypothesis.

Since theP-value, we fail to reject the null hypothesis.