Question 12.35

35. Missing Values. Part of an ANOVA table for an analysis of variance involving 7 groups for a study follows; each sample contained 10 data values.

Source of variation	Sum of square	Degrees of freedom	Mean squares	$F$
Treatment	120	—	—	—
Error	315	—	—
Total	—

Find all six missing values in the table and fill in the blanks.
Perform the appropriate hypothesis test using $α = 0.05$ .

12.1.35

(a) Missing values are in red.

Source of variation	Sum of squares	Degrees of freedom	Mean square	$F$
Treatments	120	6	20	4
Error	315	63	5
Total	435

(b) $H_{0} : μ_{1} = μ_{2} = μ_{3} = μ_{4} = μ_{5} = μ_{6} = μ_{7}$ . $H_{a}$ : Not all the population means are equal. Reject $H_{0}$ if the $p -value \leq 0.05$ . $F_{data} = 4$ $p -value = 0.0018680725$ . Since the $p -value \leq 0.05$ , we reject $H_{0}$ . There is evidence that not all the population means are equal.