T-test for two sample assuming equal variances Calculator
Note: This calculator is for testing using sample mean and sd. If you only have sample values use TWO SAMPLE TEST FROM SAMPLE VALUES calculator
You can see a sample solution below. Enter your data to get the solution for your question
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$$ \displaylines{ \mathbf{\color{Red}{2\;tail\;test}}
\\ \\
x1 = 6
\\ \\
x2 = 5
\\ \\
n1 = 4
\\ \\
n2 = 4
\\ \\
s1 = 2
\\ \\
s2 = 2
\\ \\
\alpha = 0.05
\\ \\
H_{0}: \mu_{1} = \mu_{2}
\\ \\
H_{a}: \mu_{1} \neq \mu_{2}
\\ \\
Assuming\;equal\;variances,\;So\;pooled\;standard\;deviation\;=\;s_{p}
\\ \\ \Rightarrow
\sqrt{\frac{(n_{1}-1)s_{1}^{2} + (n_{2}-1)s_{2}^{2}}{n_{1}+n_{2}-2}}
\\ \\ \Rightarrow
\sqrt{\frac{(4-1)2^{2} + (4-1)2^{2}}{4+4-2}}
\\ \\ \Rightarrow
\sqrt{\frac{24}{6}}
\\ \\ \Rightarrow
\sqrt{4.0}
\\ \\ \Rightarrow
2.0
\\ \\
t=
\frac{x1-x2}{s_{p} \sqrt{\frac{1}{n_{1}}+\frac{1}{n_{2}}}}
\\ \\
\\ \\ \Rightarrow
\frac{6-5}{2.0 \sqrt{\frac{1}{4}+\frac{1}{4}}}
\\ \\
\\ \\ \Rightarrow
\frac{1}{1.414214}
\\ \\
\\ \\ \Rightarrow
0.707107
\\ \\
df=n1+n2-2=
4 + 4 -2
\\ \\ \Rightarrow
6
\\ \\
Critical\;values\;are\; 2.446912 -2.446912
\\ \\
p= 0.506021
\\ \\
The\;result\;is\;not\;significant\;at\;p\;<\;0.05.\;So\;Failed\;to\;Reject\;H_{0}
} $$