Directions: Solve the following problems completely.

1.The proportion of students who passed an engineering examination was 80%.

Students complained that they would have done better if they were allowed to use

calculators. Later, a random sample of 90 students took this exam with calculators and 75

passed. Was this a significant improvement at 0.05 level?

2.It is claimed that the average time spent by employees on telephone calls is less

than 6 minutes. In a study time spent on the telephone by its employees, a large office

monitors a random sample of 27 employee calls and finds the mean length of these calls to

be 5.8 minutes with a standard deviation of 1.4 minutes. Is the claim true at 0.05 level of

significance?