${s}_{p}=\sqrt{\frac{\left({n}_{1}-1\right){s}_{1}^{2}+\left({n}_{2}-1\right){s}_{2}^{2}}{\left(n+n-2\right)}}=\sqrt{\frac{\left(100-1\right)\text{\hspace{0.17em}\hspace{0.17em}}{\text{\hspace{0.17em}}8.4}^{2}+\left(100-1\right){\text{\hspace{0.17em}}\text{\hspace{0.17em}}7.7}^{2}}{\left(100+100-2\right)}}=8.1$

Description:

Math equation. This shows the equation for Sp, the pooled estimate of the common standard deviation, and it then substitutes the values for this problem. Both sample sizes are 100; the first standard deviation is 8.4, and the second is 7.7. So Sp equals the square root of a quotient whose numerator is (100-1) times 8,4 squared plus (100-1) times 7.7 squared. The denominator is 100+100-2. The final answer is 8.1.