# In order to test the difference in populations means, samples were collected for two independent populations where the variances are assumed unknown and equal and the population normally distributed. The following data resulted: Sample 1 - x_1 = 112, s_1 = 14, n_1 = 25 Sample 2 - x_2 = 107, s_2 = 17, n_2 =28 The value of the pooled standard deviation is approximately 15.66. True or False?

In order to test the difference in populations means, samples were collected for two independent populations where the variances are assumed unknown and equal and the population normally distributed. The following data resulted:
Sample 1 -
${x}_{1}=112,{s}_{1}=14,{n}_{1}=25$
Sample 2 -
${x}_{2}=107,{s}_{2}=17,{n}_{2}=28$

The value of the pooled standard deviation is approximately 15.66. True or False?
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Zayne Wagner
Pooled standard deviation:
${S}_{pooled}=\sqrt{\frac{\left({n}_{1}-1\right){S}_{1}^{2}+\left({n}_{2}-1\right){S}_{2}^{2}}{{n}_{1}+{n}_{2}-2}}$
Therefore,
${S}_{pooled}=\sqrt{\frac{\left(25-1\right){14}^{2}+\left(28-1\right){17}^{2}}{25+28-2}}\phantom{\rule{0ex}{0ex}}=\sqrt{245.2353}\phantom{\rule{0ex}{0ex}}=15.66$
Thus, the statement “The value of the pooled standard deviation is approximately 15.66” is true.