Question

An automobile manufacturer wants to determine what proportion of its customers are dissatisfied with the service received from their local dealer. The manufacturer’s manager doesn’t have any estimate for the proportion of dissatisfied customers. How many customers should they sample if they want to be correct to within 4% of the actual proportion with a 98% level of confidence?

Answer 1

Solution :

Given that,

= 0.5

1 - = 0.5

margin of error = E = 4% = 0.04

At 98% confidence level the z is,

= 1 - 98%

= 1 - 0.98 = 0.02

/2 = 0.01

Z/2 = 2.326 ( Using z table )

Sample size = n = (Z/2 / E)2 * * (1 - )

= (2.326 / 0.04)2 * 0.5 * 0.5

=845.35

Sample size = 845 rounded