a Concentrations of nitrogen oxides and of hydrocarbons in g

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

Solution

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