An automobile manufacturer would like to know what proportion of its customers are dissatisfied with the service received from their local dealer. The customer relations department will survey a random sample of customers and compute a 95% confidence interval for the proportion that are dissatisfied. From past studies, they believe that this proportion will be about 0.2.
a) Find the sample size needed if the margin of error for the confidence interval half-width to be about 0.03.
b) After taking this survey, suppose 11% of the sample say that they are dissatisfied.
What is the margin of error for the 95% confidence interval?
Use 4 decimal places.