A fast food restaurant has been considering dropping the pickles from its burgers. There is some sentiment that
the ubiquitous pickle adds to the cost of the sandwich, but most people remove them anyway. The CEO decides that if we can be reasonably certain more than two-thirds of customers remove the pickle, then the pickle should no longer be placed on the sandwich (except by request). The operation manager was enlisted to spy on a random sample of one thousand customers. He found that 70 percent removed the pickle.
If the management wants to use confidence interval concept, to decide what they should do:
In what percentage of confidence level below that we can NOT be sure that more than two-thirds of customers remove the pickle?