Answer
$-t_{\frac{α}{2}}\lt t_0\lt t_{\frac{α}{2}}$: null hypothesis is not rejected.
There is not enough evidence to conclude that the rate of return between value funds and growth funds differ.
Work Step by Step
$x ̅_1,n_1~and~s_1$ refer to value funds and $x ̅_2,n_2~and~s_2$ refer to growth funds.
$x ̅_1=\frac{∑x_{1_i}}{n_1}=8.653$
$s_1=\sqrt {\frac{∑(x_{1_i}-x ̅_1)^2}{n_1-1}}=2.295$
$x ̅_2=\frac{∑x_{2_i}}{n_2}=8.206$
$s_2=\sqrt {\frac{∑(x_{2_i}-x ̅_2)^2}{n_2-1}}=0.726$
$H_0:~µ_1=µ_2$ versus $H_1:~µ_1\ne µ_2$
$t_0=\frac{(x ̅_1-x ̅_2)-(µ_1-µ_2)}{\sqrt {\frac{s^2_1}{n_1}+\frac{s^2_2}{n_2}}}=\frac{(8.653-8.206)-0}{\sqrt {\frac{2.295^2}{10}+\frac{0.726^2}{10}}}=0.587$
$n=10$, so:
$d.f.=n-1=9$
Two-tailed test:
$t_{\frac{α}{2}}=t_{0.025}=2.262$
(According to Table VI, for d.f. = 9 and area in right tail = 0.025)
Also, $-t_{\frac{α}{2}}=-2.262$
Since $-t_{\frac{α}{2}}\lt t_0\lt t_{\frac{α}{2}}$, we do not reject the null hypothesis.
