Example 8.6.1 Roman Pottery in Britain. Tubb, Parker, and Nickless (1980) describe a study of samples of pottery from the Roman era found in various location in Great Britain. One measurement made on each sample of pottery was the percentage of the sample that was aluminum oxide. Suppose that we are interested in comparing the aluminum oxide percentages at two different locations. There were … samples analyzed from Llanederyn with sample average of … and … Another … sample came from Ashley Rails with … and … . Suppose that we model the data as normal random variables with two different means … and … but common variance … We want to test the null hypothesis … against the alternative hypothesis … The observed value of … defined by Eq. (8.6.3) is – 6.302. From the table of the … distribution in this book with … degrees of freedom, we find that … , and … So, we would reject … at any level … Indeed, the p – value associated with this value of. … is about …