Sleep. In 1908, W. S. Gosset published the article “The Probable Error of a Mean” (Biometrika, Vol. 6, pp. 1–25). In this pioneering paper, written under the pseudonym “Student,” Gosset 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 a sample of 10 patients using laevohysocyamine hydrobromide. 1.9 0.8 1.1 0.1 −0.1 4.4 5.5 1.6 4.6 3.4

a. Obtain and interpret a 95% confidence interval for the additional sleep that would be obtained on average for all people using laevohysocyamine hydrobromide. (Note: x¯ = 2.33 hr;

s = 2.002 hr.)

b. Was the drug effective in increasing sleep? Explain your answer.