2.) You want to know if there are geographic differences in lead levels in drink

Question

2.) You want to know if there are geographic differences in lead levels in drinking water. You divide the city into 4 quadrants (NE, NW, SE, and SW) and measure lead levels in 10 sites in each quadrant. a.) Complete the ANOVA table below based on the experiment described. (20) Sum of Degrees of Mean F F(critical) Significant? Y/N Between 120 Within Total 200 b.) If the F value was significant (disregard your answer above), what could you conclude about lead levels in the drinking water in the city? (5) C.) If the F value was significant (disregard your answer above), what would be your next step statistically? (What test or tests) (5)

Explanation / Answer

Claim : To test whether there is mean geographic diffrences in lead levels of drinking water.

2Hypothesis : Ho: All groups has equal mean

H1 : Atleast one group has different mean

By using One way ANOVA we can compute it

Given that , total number of quaderants = k = 4

Total number measure lead levels = 4*10=40

Degrees of freedom :

For BETWEEN Df = k-1 = 3

For WITHIN Df = n-k = 40-4 = 36

For TOTAL DF = n-1 = 39

Sum of squares

1) Between = 120

2 ) Total = 200

3 ) within = Total - Between = 200-120 = 80

MEAN SQUARE

1 ) MSbetween = ( SSBetween)/Df = 120 / 3 = 40

2 )  MSwithin = ( SSwithin)/Df = 80/36 = 2.22

F_ratio = (MSBetween/MSwithin )

= ( 40 / 2.22)

= 18.02

Df = (k-1 , n-k) = ( 3 , 36)

Level of significance = 0.05

Critical value : Fc = 2.866

Decesion rule : F_ratio > Fc we Reject Ho

Yes F value is significant

Conclusion : There is sufficient evidence to conclude that there is mean geographic diffrences in lead levels of drinking water.

ORThere is sufficient evidence to conclude that atleast one group different mean.

ANOVA TABLE :

C ) F value is significant

So, Here we can use POST HOCK TEST to identify which group diifer from the rest groups.

SS DF MS F_ratio Fcritical Significant Between 120 3 40 18 2.866266 YES Within 80 36 2.222222 Total 200 39

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