Unusually high concentration of metals in drinking water can pose a health hazard. Twenty couples of data were taken from different locations of a lake measuring zinc concentration in bottom water and surface water.

Table 1. Zinc Concentration (mg/l) in bottom and surface water in different regions and areas of a lake

Location	Region	Area	Zinc_Bottom	Zinc_Surface	Zinc_Mean	TZ3_Mean
Loc 1	North	Area A	0.51	0.49	0.50	2.67
Loc 2	North	Area A	0.46	0.45	0.46	2.45
Loc 3	North	Area A	0.52	0.52	0.52	2.66
Loc 4	North	Area A	0.51	0.50	0.50	2.56
Loc 5	North	Area A	0.58	0.57	0.58	3.03
Loc 6	North	Area A	0.57	0.55	0.56	3.21
Loc 7	North	Area A	0.59	0.58	0.59	3.50
Loc 8	North	Area B	0.46	0.44	0.45	2.40
Loc 9	North	Area B	0.46	0.44	0.45	2.35
Loc 10	North	Area B	0.45	0.43	0.44	2.56
Loc11	East	Area B	0.41	0.40	0.41	1.33
Loc 12	East	Area B	0.41	0.39	0.40	1.56
Loc 13	East	Area B	0.41	0.39	0.40	1.23
Loc 14	East	Area B	0.47	0.45	0.46	1.12
Loc 15	East	Area C	0.41	0.39	0.40	1.23
Loc 16	East	Area C	0.37	0.36	0.37	1.10
Loc 17	East	Area C	0.41	0.39	0.40	1.20
Loc 18	East	Area C	0.40	0.39	0.39	1.10
Loc 19	East	Area C	0.39	0.37	0.38	1.12
Loc 20	East	Area C	0.46	0.44	0.45	1.30

Questions

Q1. Does the data suggest that the true average zinc concentration (Zinc_Mean) is different than 0.425 mg/l? Formulating your hypothesis, conduct the appropriate test and interprete your results (=0.05).

Q2. Does the data suggest that the true average concentration in the north region ishigher than that of east region? Formulating your hypothesis and providing an explanation on the reason of your choice, conduct the appropriate test and interprete your results (=0.05).

Q3. Does the data suggest that the true average concentration in the bottom water isdifferent than that of surface water? Formulating your hypothesis and providing an explanation on the reason of your test choice, conduct the appropriate test and interprete your results (=0.05).

Q4. Does the data suggest that the true average zinc concentration change due to Area? Formulating your hypothesis and providing an explanation on the reason of your choice, conduct the appropriate test and interprete your results (=0.05). If necessary, conduct a post-hoc test.

Q5. Does the data suggest that there is a relationship between Zinc concentration and TZ3 concentration? If so, fit a simple regression model which explains zinc concentration (Zinc_Mean) with TZ3 concentration (TZ3_Mean). Obtain the ANOVA table of the regression. Comment on overall significance of the model and the coefficients.

Q6. Including Region factor as a dummy variable to your previous model, fit a multiple regression model to explain zinc concentration (Zinc_Mean). Obtain the ANOVA table of the regression. Comment on overall significance of the model and the coefficients of each variable. Do you think adding Region next to TZ3_Mean improved the model? Discuss.