Sleep. In 1908, W. S. Gosset published “The Probable Error of a Mean” (Biometrika, Vol. 6, pp. 1–25). In this pioneering paper, published under the pseudonym “Student,” he introduced what later became known as Student’s t-distribution. Gosset used the following data set, which gives the additional sleep in hours obtained by 10 patients who used laevohysocyamine hydrobromide.
1.9 0.8 1.1 0.1 −0.1 4.4 5.5 1.6 4.6 3.4

a. At the 5% significance level, do the data provide sufficient evidence to conclude that laevohysocyamine hydrobromide is effective in increasing sleep?

b. Repeat part

(a) at the 1% significance level.