Question

You are hired by a local company to determine if people feel more confident in the provincial or federal government. You ask several people who live in St Catharines how confident they are that the provincial government is doing a good job (out of 50, higher numbers are better). You then ask them about their confidence in the federal government and get the following data. What would you conclude?

	Provincial	Federal	D	D2
	26	38	-12	144
	25	29	-4	16
	25	33	-8	64
	28	24	4	16
	24	31	-7	49
	21	30	-9	81
	19	19	0	0
	38	46	-8	64
	29	40	-11	121
	41	31	10	100
	21	29	-8	64
	28	37	-9	81
	36	39	-3	9
Sum	361	426	-65	809
SS	550.3077	620.3077	484	23436.31

Answer 1

From the given data below:

	Provincial	Federal	D	D^2
	26	38	-12	144
	25	29	-4	16
	25	33	-8	64
	28	24	4	16
	24	31	-7	49
	21	30	-9	81
	19	19	0	0
	38	46	-8	64
	29	40	-11	121
	41	31	10	100
	21	29	-8	64
	28	37	-9	81
	36	39	-3	9
Sum >>	361	426	-65	809
SS	550.3077	620.3077	484	23436.31

At first we need to construct an ANOVA table to test the Hypothesis, whether there is a significant variance between people's choice on performance of Provincial Government is equal or not equal to performance of Federal Government.

Let deonotes the average performance of Provincial Government and is the average performance of Federal Government.

The stated Hypothesis are

against the alternative

From the above data, we construct the following one-way ANOVA table

Note: We have used the first two colums to construct the ANOVA table

SUMMARY
Groups	Count	Sum	Average	Variance
Provincial	13	361	27.76923	45.85897
Federal	13	426	32.76923	51.69231
ANOVA
Source of Variation	SS	df	MS	F observed	P-value	F crit
Between Groups (Two Govts)	162.5	1	162.5	3.331581	0.080433	4.259677
Within Groups (error)	1170.615	24	48.77564
Total	1333.115	25

Since the observed value of F < F Critical at 0.05 level of significance, we conclude that, there is no signifacnce difference between the two governments as perceived by the people who were responded