Samples Were Drawn from Three Populations $n _ { 1 } = 6 , n _ { 2 } = 9$

Samples were drawn from three populations. The sample sizes were $n _ { 1 } = 6 , n _ { 2 } = 9$ , and $n _ { 3 } = 8$ . The sample means were $\bar { x } _ { 1 } = 1.52 , \bar { x } _ { 2 } = 1.62$ , and $\bar { x } _ { 3 } = 1.65$ . The sample standard deviations were $s _ { 1 } = 0.50 , s _ { 2 } = 0.36$ , and $s _ { 3 } = 0.48$ . The grand mean is $\bar { x } = 1.604348$ .
Compute the value of the test statistic $F$ .

A) 0.158
B) 0.031
C) 3.900
D) 0.062