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Do the desks share a mean

StatisticsHard

Desk A has $9$ daily results with average $5$ , and desk B has $9$ with average $2$ . All results are independent and normal with known standard deviation $6$ . Testing that the desks share one mean against separate means, what is the value of $- 2 log Λ$ ? Give a fraction.

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Hint

The statistic is the drop in the sum of squared residuals, divided by $σ^{2}$ .

Solution

The shared fit is $\frac{5 + 2}{2} = \frac{7}{2}$ , so each desk's average sits $\frac{3}{2}$ from it.
Moving to separate means removes $18 \times \frac{9}{4} = \frac{81}{2}$ from the sum of squared residuals.
Dividing by $36$ gives $\frac{\frac{81}{2}}{36} = \frac{9}{8}$ .

Answer: $\frac{9}{8}$

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