Question: 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. Find a \(95 \%\) confidence interval for the additional sleep that would be obtained on average for all people using laevohysocyamine hydrobromide. (Note: \(\bar{x}=2.33 \mathrm{hr} ;\) \(s=2.002 \mathrm{hr}\).)
2. Was the drug effective in increasing sleep? Explain your answer.

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