Question

A mid-size city must decide whether or not to build a new combined bus and train station. To build the new station will require an increase in city taxes. According to a city politician, 70% of all city residents support the tax increase to build a combined bus and train station. An opinion poll of 400 city residents will ask whether they favor a rise in taxes to pay for a combined bus and train station.

What is the standard deviation of the distribution of sample proportions?

Answer 1

Solution

Given that,

p = 0.70

1 - p = 1-0.70=0.30

n = 400

standard deviation of the distribution of sample proportion= =  [p( 1 - p ) / n] = [(0.70*0.30) / 400 ] = 0.0229

standard deviation of the distribution of sample proportion= =0.0229