A consumer group hoping to assess customer experiences with auto dealer surveys 167 people who recently bought new cars; 3% of them expressed dissatisfaction with the salesperson. We want to learn about the general opinion towards the salesperson. a) Please construct a 90% score confidence interval for the population proportion of dissatisfaction and interpret it.
b) Please construct a 90% traditional confidence interval.
c) If we want to control the width of the 90% score confidence interval to be within 0.02, how large a sample do we need? Please use the conservative method.
d) If we increase the confidence level from 90% to 95%, will the width of CI be increased or decreased? Why?