Question

A. We have 3 stratums with σ12=15,σ22=225,σ32=100. Estimate the total population τ with bound of error 400. Choose appropriate sample size and equal number of observations taken from each stratum.

B. The company want to evaluate the population mean in county with 3 cities. They chose 3 stratums in each of the cities. The σ1,σ2,σ3 are resp. 5,15 and 10. Bond of error is 2. The cost for obtaining observation in all areas is the same. Find the appropriate sample size n and allocation of n.

C. The CSI has a lab, which studies behavior of naked mole rats. These animals are divided in 2 groups by sex – male and female. The number of males is 400 and the females are 500. In order to get variability in each group the researcher measures the weight difference between smallest and largest rat in each group (male, female) and founds that for males group the difference is 10 grams for females it is 8 grams.   The cost of obtaining the observation is the same for all groups. How large the sample should be in order to estimate the population average with error bound of 1 gram?  

D. The survey company has only $500 budget and want to make a survey of bread consumption in 2 cities, 1 village and rural area. The cost per observation is c1=5,c2=7,c3=1,c4=16. The stratums standard deviations are respectively 5,15,10 and 7. Chose the sample and allocation that minimizes V(yst) (V(mean of sample)).

E For 3 strata A,B,C using table in slide 18 for the data, and assuming expenses per observation/per strata c1=c2=9, c3=16 calculate the number of samples n and the strata samples n1,n2,n3 which give the desired bound of error at minimum cost. The stratums have resp. 155,62 and 93 units.

Any answers help. Thank you!

Answer 1