Question 12.21

For Exercises 15–22, do the following for the indicated data.

Calculate the following:
1. $SSTR = Σ n_{i} {(\bar{x} - \bar{\bar{x}})}^{2}$
2. $SSE = Σ (n_{i} - 1) s_{i}^{2}$
3. $SST = SSTR + SSE$
4. ${df}_{1} = k - 1$
5. ${df}_{2} = n_{t} - k$
6. $MSTR = SSTR / {df}_{1}$
7. $MSE = SSE / {df}_{2}$
Construct the ANOVA table using the statistics computed in (a).

Question 12.21

21.

Sample A	Sample B	Sample C	Sample D
${\bar{x}}_{A} = 50$	${\bar{x}}_{B} = 75$	${\bar{x}}_{C} = 100$	${\bar{x}}_{D} = 125$
$s_{A} = 5$	$s_{B} = 4$	$s_{C} = 6$	$s_{D} = 5$
$n_{A} = 100$	$n_{B} = 150$	$n_{C} = 200$	$n_{D} = 150$

12.1.21

(a) (i) SSTR = 395,833.3333 (ii) SSE = 15,748 (iii) SST = 411,581.3333 (iv) ${df}_{1} = 3$ (v) ${df}_{2} = 596$ (vi) MSTR = 131,944.4444 (vii) MSE = 26.4228

(b)

Source of variation	Sum of squares	Degrees of freedom	Mean square	$F$
Treatments	395,833.3333	3	131,944.4444	4993.5794
Error	15,748	594	26.4228
Total	411,581.3333