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. Identify the variable under consideration.

b. Identify the two populations.

c. Identify the paired-difference variable.

d. Are the numbers in the table paired differences? Why or why not?

e. At the 5% significance level, do the data provide sufficient evidence to conclude that laevohysocyamine hydrobromide is effective in increasing sleep? (Note: d = 2.33 and sd = 2.002.)

f. Repeat part

(e) at the 1% significance level.