34.5 Example: Removal efficiency
In wastewater treatment facilities, air from biofiltration is passed through a membrane and dissolved in water, and is transformed into harmless byproducts. The removal efficiency y (in %) may depend on the inlet temperature (in ∘C; x).
The RQ is
In treating biofiltation wastewater, is the removal efficiency associated with the inlet temperature?
The population parameter is ρ, the correlation between the removal efficiency and inlet temperature.
A scatterplot of n=32 samples (Fig. 34.9) suggests an approximately linear relationship (Chitwood and Devinny 2001; Devore and Berk 2007). The output (jamovi: Fig. 34.10; SPSS: Fig. 34.11) shows that the sample correlation coefficient is r=0.891, and so R2=(0.891)2=79.4%. This means that about 79.4% of the variation in removal efficiency can be explained by knowing the inlet temperature.
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FIGURE 34.9: The relationship between removal efficiency and inlet temperature
To test if a relationship exists in the population, write:
- H0: ρ=0;
- H1: ρ≠0: Two-tailed (as implied by the RQ).
The software output (jamovi: Fig. 34.10; SPSS: Fig. 34.11) shows that P<0.001 (which is what P=0.000 in SPSS means). We conclude:
The sample presents very strong evidence (two-tailed P<0.001) that removal efficiency depends on the inlet temperature (r=0.891; n=32) in the population.
The relationship is approximately linear and there is no obvious non-constant variance, and the sample size is larger than 25, so the hypothesis test results will be statistically valid.

FIGURE 34.10: jamovi output for the removal-efficiency data
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FIGURE 34.11: SPSS output for the removal-efficiency data