In this article, a combined general family of estimators is proposed for estimating finite population mean of a sensitive variable in stratified random sampling with non-sensitive auxiliary variable based on randomized response technique. Under stratified random sampling without replacement scheme, the expression of bias and mean square error (MSE) up to the first-order approximations are derived. Theoretical and empirical results through a simulation study show that the proposed class of estimators is more efficient than the existing estimators, i.e., usual stratified random sample mean estimator, Sousa et al (2014) ratio and regression estimator of the sensitive variable in stratified sampling.

Recently, nanomaterials have received considerable attention in the agricultural sector, due to their distinctive characteristics such as small size, high surface area to volume ratio, and charged surface. These properties allow nanomaterials to be utilized as nanofertilizers, that can improve crop nutrient management and reduce environmental nutrient losses. However, after soil application, metallic nanoparticles have been shown to be toxic to soil biota and their associated ecosystem services. The organic nature of nanobiochar (nanoB) may help to overcome this toxicity while maintaining all the beneficial effects of nanomaterials. We aimed to synthesize nanoB from goat manure and utilize it with CuO nanoparticles (nanoCu) to influence soil microbes, nutrient content, and wheat productivity. An X-ray diffractogram (XRD) confirmed nanoB synthesis (crystal size = 20 nm). The XRD spectrum showed a distinct carbon peak at 2θ = 42.9°. Fourier-transform spectroscopy of nanoB’s surface indicated the presence of C=O, C≡N–R, and C=C bonds, and other functional groups. The electron microscopic micrographs of nanoB showed cubical, pentagonal, needle, and spherical shapes. NanoB and nanoCu were applied alone and as a mixture at the rate of 1000 mg kg−1 soil, to pots where wheat crop was grown. NanoCu did not influence any soil or plant parameters except soil Cu content and plant Cu uptake. The soil and wheat Cu content in the nanoCu treatment were 146 and 91% higher, respectively, than in the control. NanoB increased microbial biomass N, mineral N, and plant available P by 57, 28, and 64%, respectively, compared to the control. The mixture of nanoB and nanoCu further increased these parameters, by 61, 18, and 38%, compared to nanoB or nanoCu alone. Consequently, wheat biological, grain yields, and N uptake were 35, 62 and 80% higher in the nanoB+nanoCu treatment compared to the control. NanoB further increased wheat Cu uptake by 37% in the nanoB+nanoCu treatment compared to the nanoCu alone. Hence, nanoB alone, or in a mixture with nanoCu, enhanced soil microbial activity, nutrient content, and wheat production. NanoB also increased wheat Cu uptake when mixed with nanoCu, a micronutrient essential for seed and chlorophyll production. Therefore, a mixture of nanobiochar and nanoCu would be recommended to farmers for improving their clayey loam soil quality and increasing Cu uptake and crop productivity in such agroecosystems.