Question

Stats I, Item # Q-08

Saleemah, the assistant superintendent in charge of reviewing staffing patterns, is investigating the number of substitute teachers assigned daily to the elementary schools in the district. She ponders whether the numbers vary by school and/or by day of the week. She tests her claims at the 10% significance level, and presumes that the underlying data collection is normally distributed. She gathers independent, simple random samples. The following data represent the numbers of substitute teachers assigned daily to each school during a randomly selected week, cross referenced by school and day of the week:

What are the claims is she testing? What conclusions should she draw? Explain in detail for both factors, both technically and contextually. In particular, if the findings for either one of the two or both factors are especially marginal or strong, please note those results. Cite relevant critical values and p-values that support the findings.

	PS#1	PS#2	PS#3	PS#4	PS#5	PS#6	PS#7	PS#8
Mondays	4	8	7	6	2	9	12	8
Tuesdays	5	6	7	4	5	7	10	8
Wednesdays	6	4	7	4	4	5	8	8
Thursdays	7	6	7	4	3	3	6	8
Fridays	3	8	7	6	6	1	4	8

Answer 1

Anova: Two-Factor Without Replication
SUMMARY	Count	Sum	Average	Variance
Mondays	8	56	7	9.428571429
Tuesdays	8	52	6.5	3.714285714
Wednesdays	8	46	5.75	3.071428571
Thursdays	8	44	5.5	3.714285714
Fridays	8	43	5.375	6.267857143
PS#1	5	25	5	2.5
PS#2	5	32	6.4	2.8
PS#3	5	35	7	0
PS#4	5	24	4.8	1.2
PS#5	5	20	4	2.5
PS#6	5	25	5	10
PS#7	5	40	8	10
PS#8	5	40	8	0
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
days	15.6	4	3.9	1.087649402	0.381652762	2.7140758
PS	82.975	7	11.85357143	3.305776892	0.010850475	2.35925985
Error	100.4	28	3.585714286
Total	198.975	39

claims

not all means at each day are same

not all mean at each PS are same

p-value of days =   0.3817 > 0.10 (alpha)

hence we fail to reject the null hypothesis

p-value of PS= 0.010850475 < 0.10

hence we reject the null hypothesis

we conclude that not all mean at each PS are same