 # Test whether the claim that the two sample groups come from populations with the cistG 2021-10-17 Answered
Test whether the claim that the two sample groups come from populations with the same mean or not.
You can still ask an expert for help

• Questions are typically answered in as fast as 30 minutes

Solve your problem for the price of one coffee

• Math expert for every subject
• Pay only if we can solve it irwchh
State the test hypotheses.
Let first population denote the treatment and the second population denote the placebo.
Null hypothesis:
${H}_{0}:{\mu }_{1}={\mu }_{2}$
Alternative hypothesis:
${H}_{1}:{\mu }_{1}\ne {\mu }_{2}$
Test statistic:
The test statistic formula is,
$t=\frac{\left({\stackrel{―}{x}}_{1}-{\stackrel{―}{x}}_{2}\right)-\left({\mu }_{1}-{\mu }_{2}\right)}{\sqrt{\frac{{s}_{p}^{2}}{{n}_{1}}+\frac{{s}_{p}^{2}}{{n}_{2}}}}$
Where ${s}_{p}^{2}=\frac{\left({n}_{1}-1\right){s}_{1}^{2}+\left({n}_{2}-1\right){s}_{2}^{2}}{\left({n}_{1}-1\right)+\left({n}_{2}-1\right)}$
With degrees of freedom $df={n}_{1}+{n}_{2}-2$
Let ${\stackrel{―}{x}}_{1}$ denotes the first sample mean, ${\stackrel{―}{s}}_{1}$ denotes the first sample standard deviation, ${n}_{1}$ denotes the first sample size, ${\stackrel{―}{x}}_{2}$ denotes the second sample mean, ${s}_{2}$ denotes the second sample standard deviation, ${n}_{2}$ denotes the second sample size, ${\mu }_{1}$ denotes the first sample population mean, and ${\mu }_{2}$ denotes the second sample population mean.
The pooled sample variance is,
${s}_{p}^{2}=\frac{\left({n}_{1}-1\right){s}_{1}^{2}+\left({n}_{2}-1\right){s}_{2}^{2}}{\left({n}_{1}-1\right)+\left({n}_{2}-1\right)}$
$=\frac{\left(22-1\right){\left(0.015\right)}^{2}+\left(22-1\right){\left(0.000\right)}^{2}}{\left(22-1\right)+\left(22-1\right)}$
$=\frac{0.004725+0}{42}$
$=0.0001125$
Substitute ${n}_{1}=22{\stackrel{―}{x}}_{1}=0.049,{s}_{p}^{2}=0.0001125,{n}_{2}=22$ and ${\stackrel{―}{x}}_{2}=0.000$ in the test statistic formula
$t=\frac{\left(0.049-0.000\right)}{\sqrt{\frac{0.0001125}{22}+\frac{0.0001125}{22}}}$
$=\frac{0.049}{0.0032}$