Samples Were Drawn from Three Populations $n _ { 1 } = 8 , n _ { 2 } = 7$

Samples were drawn from three populations. The sample sizes were $n _ { 1 } = 8 , n _ { 2 } = 7$ , and $n _ { 3 } = 5$ . The sample means were $\bar { x } _ { 1 } = 1.84 , \bar { x } _ { 2 } = 1.98$ , and $\bar { x } _ { 3 } = 1.72$ . The sample standard deviations were $s _ { 1 } = 0.43 , s _ { 2 } = 0.30$ , and $s _ { 3 } = 0.30$ . The grand mean is $\bar { x } = 1.859$ . Compute the value of the test statistic F.

A) 0.782
B) 2.194
C) 0.101
D) 0.202