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# 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

Mean of Sample 1: One tailed Two tailed

## You can see a sample solution below. Enter your data to get the solution for your question

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$$\displaylines{ \mathbf{\color{Red}{2\;tail\;test}} \\ \\ x1 = 6 \\ \\ x2 = 5 \\ \\ n1 = 4 \\ \\ n2 = 4 \\ \\ s1 = 2 \\ \\ s2 = 2 \\ \\ \alpha = 0.05 \\ \\ H_{0}: \mu_{1} = \mu_{2} \\ \\ H_{a}: \mu_{1} \neq \mu_{2} \\ \\ Assuming\;equal\;variances,\;So\;pooled\;standard\;deviation\;=\;s_{p} \\ \\ \Rightarrow \sqrt{\frac{(n_{1}-1)s_{1}^{2} + (n_{2}-1)s_{2}^{2}}{n_{1}+n_{2}-2}} \\ \\ \Rightarrow \sqrt{\frac{(4-1)2^{2} + (4-1)2^{2}}{4+4-2}} \\ \\ \Rightarrow \sqrt{\frac{24}{6}} \\ \\ \Rightarrow \sqrt{4.0} \\ \\ \Rightarrow 2.0 \\ \\ t= \frac{x1-x2}{s_{p} \sqrt{\frac{1}{n_{1}}+\frac{1}{n_{2}}}} \\ \\ \\ \\ \Rightarrow \frac{6-5}{2.0 \sqrt{\frac{1}{4}+\frac{1}{4}}} \\ \\ \\ \\ \Rightarrow \frac{1}{1.414214} \\ \\ \\ \\ \Rightarrow 0.707107 \\ \\ df=n1+n2-2= 4 + 4 -2 \\ \\ \Rightarrow 6 \\ \\ Critical\;values\;are\; 2.446912 -2.446912 \\ \\ p= 0.506021 \\ \\ The\;result\;is\;not\;significant\;at\;p\;<\;0.05.\;So\;Failed\;to\;Reject\;H_{0} }$$