n 1 = 16 n 2 = 16 n 1 = 10 n 2 = 9 x ˉ 1 = 30.125 x ˉ 2 = 35.6875 s 1 2 = 46.7833 s 2 2 = 106.3625 ν = ( s 1 2 n 1 + s 2 2 n 2 ) 2 1 n 1 − 1 ( s 1 2 n 1 ) 2 + 1 n 2 − 1 ( s 2 2 n 2 ) 2 = ( 46.7833 16 + 106.3625 16 ) 2 1 15 ( 46.7833 16 ) 2 + 1 15 ( 106.3625 16 ) 2 = 26.0564 ∼ 26 T = x ˉ 1 − x ˉ 2 s 1 2 n 1 + s 2 2 n 2 = 30.125 − 35.6875 46.7833 16 + 106.3625 16 = − 1.79795 P ( ∣ t ∣ > 1.79795 ) = 2 F t , 26 ( − 1.79795 ) = 2 ⋅ 0.0419 = 0.0838 > 0.05 ⇒ ⇒ t h e d i f f e r e n c e i s n o t s i g n i f i c a n t n_1=16\\n_2=16\\n_1=10\\n_2=9\\\bar{x}_1=30.125\\\bar{x}_2=35.6875\\{s_1}^2=46.7833\\{s_2}^2=106.3625\\\nu =\frac{\left( \frac{{s_1}^2}{n_1}+\frac{{s_2}^2}{n_2} \right) ^2}{\frac{1}{n_1-1}\left( \frac{{s_1}^2}{n_1} \right) ^2+\frac{1}{n_2-1}\left( \frac{{s_2}^2}{n_2} \right) ^2}=\frac{\left( \frac{46.7833}{16}+\frac{106.3625}{16} \right) ^2}{\frac{1}{15}\left( \frac{46.7833}{16} \right) ^2+\frac{1}{15}\left( \frac{106.3625}{16} \right) ^2}=26.0564\sim 26\\T=\frac{\bar{x}_1-\bar{x}_2}{\sqrt{\frac{{s_1}^2}{n_1}+\frac{{s_2}^2}{n_2}}}=\frac{30.125-35.6875}{\sqrt{\frac{46.7833}{16}+\frac{106.3625}{16}}}=-1.79795\\P\left( \left| t \right|>1.79795 \right) =2F_{t,26}\left( -1.79795 \right) =2\cdot 0.0419=0.0838>0.05\Rightarrow \\\Rightarrow the\,\,difference\,\,is\,\,not\,\,significant n 1 = 16 n 2 = 16 n 1 = 10 n 2 = 9 x ˉ 1 = 30.125 x ˉ 2 = 35.6875 s 1 2 = 46.7833 s 2 2 = 106.3625 ν = n 1 − 1 1 ( n 1 s 1 2 ) 2 + n 2 − 1 1 ( n 2 s 2 2 ) 2 ( n 1 s 1 2 + n 2 s 2 2 ) 2 = 15 1 ( 16 46.7833 ) 2 + 15 1 ( 16 106.3625 ) 2 ( 16 46.7833 + 16 106.3625 ) 2 = 26.0564 ∼ 26 T = n 1 s 1 2 + n 2 s 2 2 x ˉ 1 − x ˉ 2 = 16 46.7833 + 16 106.3625 30.125 − 35.6875 = − 1.79795 P ( ∣ t ∣ > 1.79795 ) = 2 F t , 26 ( − 1.79795 ) = 2 ⋅ 0.0419 = 0.0838 > 0.05 ⇒ ⇒ t h e d i ff ere n ce i s n o t s i g ni f i c an t
Comments
Leave a comment