Question

A market researcher for a provider of music player accessories wants to know the proportion of customers who own cars to assess the market for a new car charger. A survey of 400 customers indicates that 79​% own cars. ​

a) What is the estimated standard deviation of the sampling distribution of the​ proportion?

​b) How large would the estimated standard deviation have been if he had surveyed only 100 customers​ (assuming the proportion is about the​ same)?

Answer 1

Solution

Given that,

p = 0.79

1 - p = 1 - 0.79 = 0.21

a) n = 400

=  [p( 1 - p ) / n] = [(0.79 * 0.21) / 400 ] = 0.0204

b) n = 100

=  [p( 1 - p ) / n] = [(0.79 * 0.21) / 100 ] = 0.0407