Statistics

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Solve the questions using a Statistics package (Excel etc.). Please make sure that you provide comments/explanations about your decisions.

 

Unusually high concentration of metals in drinking water can pose a health hazard. Twenty couples of data were taken from different locations of Kuş Cenneti 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 Karacakaçan 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 (α=0.05). (15p)

Q2. Does the data suggest that the true average concentration in the north region is higher 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 (α=0.05). (15p)

Q3. Does the data suggest that the true average concentration in the bottom water is different 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 (α=0.05). (15p)