a) Concentrations of nitrogen oxides and of hydrocarbons (in ?g/m3) were determi

Question

a) Concentrations of nitrogen oxides and of hydrocarbons (in ?g/m3) were determined in a certain urban
area. Please test the hypothesis that both classes of air pollutants were present at the same concentration
using a nonparametric test.

b) The data are the days for seven cockroach eggs to hatch at one laboratory temperature and for eight
eggs to hatch at another temperature. Please use a non-parametric test on the null hypothesis that the
hatch duration is independent of temperature.

*Please use excel and provide all of the steps

6 Days nitrogen oxides 104 116 84 77 6 848172 6 97 84 hydrocarbons 108 118 89 7 66 8388 10 11 76 68 9681

Explanation / Answer

Null hypothesis : The concentrations of nitrogen oxides andof hydrocarbons were
                         identical in that urban area.

Alternative hypothesis : The concentrations of nitrogen oxides andof hydrocarbons were
                                  not identical in that urban area.

Day Nitrogen oxides Hydrocarbons Difference Absolute diffrence Ranks 1 104 108 -4 4 5.5 2 116 118 -2 2 3 3 84 89 -5 5 7.5 4 77 71 6 6 9 5 61 66 -5 5 7.5 6 84 83 1 1 1.5 7 81 88 -7 7 10.5 8 72 76 -4 4 5.5 9 61 68 -7 7 10.5 10 97 96 1 1 1.5 11 84 81 3 3 4 Rank sum of Positivedifferences = T + = 16 Rank sum of Negativedifferences = T - = 50 Test statistic, T = Min(T + , T - ) = Min( 16, 50 ) = 16 The critical value ofthe test with 11 df is 11 Since observed T = 16> 11, we fail to reject our null hypothesis. So the concentrations ofnitrogen oxides and of hydrocarbons were identical in that urbanarea

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