You are undertaking a household travel survey for a large urban area. One of you

Question

You are undertaking a household travel survey for a large urban area. One of your key variables is the proportion of people who use bicycle for their travel, and the other key variable is the proportion of people who drive their own car. You estimate that the proportion of bicycle trips in the urban area is 0.5 percent and that the proportion of car driver trips is 61 percent. If the same accuracy is desired for each of these, of a maximum sampling error of plusminus 1/4 percentage points, what sample sizes would be required for each of these two key variables? Because of the large difference in the sample sizes, the requirements are re-evaluated. It is decided instead to specify that the requirement is for the coefficient of sample variation to be the same for each travel mode at a value of 0.025. (Recall that the coefficient of sample variation is the sampling error divided by the mean.) What are the sample sizes that are now required? How else could the error be specified that would balance the sample requirements? Illustrate with calculations to show that your method of specifying the error achieves a better balance.

Explanation / Answer

Solution :

Given ,

p=Proportion of bicycle trip in urban area is 0.5

And the proportion of car drivers trip 61%

And the sampling error is 1/4 %

You have to find the sample size (n)

Formula of sample size (n)= p*(1-p)*(Zc/E)^2

We have to find Zc for 61%

Zc for 61% is 0.28

Zc=0.28

E=sampling error=1/4 % =0.25 %=0.0025

n= 0.5*0.5*(0.28/0.0025)^2=3136

sample size(n)=3136

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