William S. Gosset was employed by the Guinness brewing company of Dublin. Sample sizes available for experimentation in brewing were necessarily small, and new techniques for handling the resulting data were needed. Gosset consulted Karl Pearson (1857-1936) of University College in London, who told him that the current state of knowledge was unsatisfactory. Gosset undertook a course of study under Pearson, and the outcome of his study was perhaps the most famous paper in statistical literature, "The Probable Error of a Mean" (1908), which introduced the t distribution.

Since Gosset was contractually bound by Guinness, he published under a pseudonym, "Student"; hence, the t distribution is often referred to asStudent's t distribution.

As an example to illustrate his analysis, Gosset reported in his paper on the results of seeding 11 different plots of land with two different types of seed: regular and kiln-dried. There is reason to believe that drying seeds before planting will increase plant yield. Since different plots of soil may be naturally more fertile, this confounding variable was eliminated by using the matched pairs design and planting both types of seed in all 11 plots.

State the appropriate hypotheses that are being tested here. Be sure to define the parameter that you are using.

Are the conditions that allow me to safely use the paired T-test satisfied? Support your answer by using appropriate visual displays which you should paste here.

Carry out the paired t-test, state the test statistic and P-value, and state your conclusion in context.