Stratified Sampling Allocation

You believe that the mean electricity usage is about twice as much for houses as for apartments or condominiums, and that the standard deviation is proportional to the mean so that S1 = 2S2 = 2S3. How would you allocate a stratified sample of 900 observations if you wanted to estimate the mean electricity consumption for all households in the city?

I'm confused as to whether this is a proportional allocation problem or a optimum allocation one. Proportional allocation formula doesn't include standard deviation anywhere

Kevin, for example for the optimun allocation:

$$S_{1}=2 \cdot S_{2} =2 \cdot S_{3}$$

$$n_{1}/n= \frac{N_{1} \cdot S_{1} } {N_{1} \cdot S_{1} + N_{2} \cdot S_{2}+ N_{3} \cdot S_{3}}=$$

$$\frac{W_{1} \cdot S_{1} } {W_{1} \cdot S_{1} + W_{2} \cdot S_{1}/2+ W_{3} \cdot S_{1}/2}=$$

$$\frac{W_{1} \cdot S_{1} } {S_{1} \cdot (W_{1} + W_{2}/2+ W_{3}/2)}=$$

$$\frac{W_{1} } { (W_{1} + W_{2}/2+ W_{3}/2)}=$$

(if $S_{i}$ is the S.D.)

• Do the standard deviations (S1 = 2S2 = 2S3) matter? – Kevin May 15 '17 at 16:18