how do you get the following null hypothesis A researcher is interested in investigating whether people perform better at dexterity tests while

listening to classical music or to no music. They design a dexterity test, and first give it to their

participants while classical music is playing, and then while no music is playing. Which hypotheses

should they use? Let ${}_1$ be the average score on the dexterity test while listening to classical music.

Let ${}_2$ be the average score on the dexterity test while not listening to music. Let ${}_d$ be the pairwise

average difference in score on the dexterity test between listening to classical music and not

listening to music, where $d=y_1-y_2.$

a$)H_0$:${}_d=0$

vs$.H_A$:${}_d>0$

b$)H_0$:${}_1-{}_2>0$

vs$.H_A$:${}_1-{}_2=0$

c$)H_0$:${}_1-{}_2=0$

vs$.H_A$:${}_1-{}_2>0$

d$)H_0$:${}_1-{}_2=0$

vs$.H_A$:${}_1-{}_{2}0$

e$)H_0$:${}_d=0$

vs$.H_A$:${}_d<mn\; id="EditorElement\_2548779">0</mn>$