The Red Lobster restaurant chain regularly surveys its customers. On the basis of these ...

     The Red   Lobster restaurant chain regularly surveys its customers.  On the   basis of these surveys, the management of the chain claims that 75% of its   customers rate the food as excellent.  A consumer testing service   wants to examine the claim by asking 460 customers to rate the   food.  What is the probability that less than 70% of customers rate   the food as being excellent?   Develop a 99 percent confidence   interval over the value of the population proportion of customers who view   the food as being excellent.  Can the claim be justified based on   this evidence at the 1 percent significance level?