Answer:
Check the explanation
Step-by-step explanation:
Going by the first attached image below we reject H_o against H_1 if obs.[tex]T > t_{\alpha /2;n-1}[/tex]
here obs.T=1.879
[tex]\therefore obs.T \ngtr 2.447=t_{0.025;6}[/tex]
we accept [tex]H_o:\mu _{1}=\mu_{2}[/tex] at 5% level of significance.
i.e there is no sufficient evidence to indicate that the special study program is more effective at 5% level of significance.
1.
this problem is simillar to the previous one except the alternative hypothesis.
Let X_i's denote the bonuses given by female managers and Y_i's denote the bonuses given by male managers.
we assume that [tex]X_i \sim N(\mu _{1},\sigma _{1}^{2}) Y_i \sim N(\mu _{2},\sigma _{2}^{2})[/tex] independently
We want to test [tex]H_0:\mu_{1}=\mu_{2} vs H_1:\mu_{1}\neq \mu_{2}[/tex]
define [tex]D_i=X_i-Y_i , i=1(1)8[/tex]
now [tex]D_i\sim N(\mu _{1}-\mu _{2}=\mu _{D},\sigma _{1}^{2}+\sigma _{2}^{2}=\sigma _{D}^{2}) , i=1(1)8[/tex]
the hypothesis becomes
[tex]H_0:\mu_{D}=0 vs H_1:\mu_{D}\neq 0[/tex]
in the third attached image, we use the same test statistic as before
i.e at 5% level of significance there is not enough evidence to indicate a difference in average bonuses .
