sp=(n11)s12+(n21)s22(n+n2)=(1001)  8.42+(1001)7.72(100+1002)=8.1


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.