Question: Sleep. In 1908, W. S. Gosset published "The Probable Error of a Mean" (Biometrika, V01. 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. Identify the variable under consideration.
2. Identify the two populations.
3. Identify the paired-difference variable.
4. Are the numbers in the table paired differences? Why or why not?
5. At the \(5 \%\) significance level, do the data provide sufficient evidence to conclude that laevohysocyamine hydrobromide is effective in increasing sleep? (Note: \(\bar{d}=\) 2.33 and \(s_{d}=2.002 .\) )
6. Repeat part (e) at the \(1 \%\) significance level.

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