Fitzgerald Reid

02/01/2024 · Elementary School

You wish to test the following claim \( \left(H_{a}\right) \) at a significance level of \( \alpha=0.001 \). For the context of this problem, \( \mu_{d}=\mu_{2}-\mu_{1} \) where the first data set represents a pre-test and the second data set represents post-test. \[ \begin{array}{l}H_{o}: \mu_{d}=0 \\ H_{a}: \mu_{d}<0\end{array} \] You believe the population of difference scores is normally distributed, but you do not know the standard deviation. You obtain pre-test and post-test samples for \( n=49 \) subjects. The average difference (post - pre) is \( \bar{d}=-2.5 \) with a standard deviation of the differences of \( s_{d}=21.5 \). What is the test statistic for this sample? (Report answer accurate to three decimal places.) test statistic \( = \)