Five samples of a ferrous-type substance are to be used to determine if there is a difference between a laboratory chemical analysis and an X-ray fluorescence analysis of the iron content. Each sample was split into two sub-samples and the two types of analysis were applied. Following are the coded data showing the iron content analysis:

Sample
Analysis 1 2 3 4 5
X-rays 2.0 2.0 2.3 2.1 2.4
Chemical 2.2 1.9 2.5 2.3 2.4

Assuming that the populations are normal, test at the 0.05 level of significance whether the two methods of analysis give, on the average, the same result.