Question 12.37

37. Missing Values. Part of an ANOVA table follows.

Source of variation	Sum of square	Degrees of freedom	Mean squares	$F$
Treatment	—	4	10	1.0
Error	—	—	—
Total	440

Find all four missing values in the table and fill in the blanks.
Perform the appropriate hypothesis test using $α = 0.10$ .

12.1.37

(a) Missing values are in red.

Source of variation	Sum of squares	Degrees of freedom	Mean square	$F$ -test statistic
Treatments	SSTR = 40	${df}_{1} = 4$	MSTR = 10	$F_{data} = 1.0$
Error	SSE = 400	${df}_{2} = 40$	MSE = 10
Total	SST = 440

(b) $H_{0} : μ_{1} = μ_{2} = μ_{3} = μ_{4} = μ_{5}$ . $H_{a}$ : Not all the population means are equal. $F_{crit} = 2.09$ . Reject $H_{0}$ if $F_{data} \geq 2.09$ . $F_{data} = 1.0$ . Since $F_{data}$ is not $\geq 2.09$ we do not reject $H_{0}$ . There is insufficient evidence that not all the population means are equal.