Test for difference between two proportions.

A bank is comparing the quality of service given by its two most important branches.  In branch A, 192 out of the random selection of 300 of its customers said that they were satisfied with the service.  In branch B, 138 out of 250 randomly selected customers said that they were satisfied with the service.

a. At the 5 percent level of significance, can we infer that branch A has a significantly higher proportion of satisfied customers than branch B? 

b. At the 5 percent level of significance, can we infer that difference in the level of satisfaction with service between the two branches is wider than 5 p.c. points?  

c. approximation with 90 percent confidence the difference in the level of satisfaction with service between the two branches.