I need to solve this statistics questions
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)
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 (α=0.05). If necessary, conduct a post-hoc test.(20 p)
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. (20p)
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.(15p)
