1. A group of employees at a large factory was asked to indicate their preference for one of two pension schemes. The table below gives the responses of three different categories of employees at the factory. Investigate at 1% level of significance whether or not there is a preference amongst the three categories. (show all work)

JOB CATEGORY PLAN A PLAN B
SUPERVISOR 10 15
CLERICAL 20 80
LABOUR 80 60

2. An airline advertises its flights between two major cities takes at most five hours. A random sample of 36 such flights gave a mean time of five hours ten minutes with a standard deviation of thirty minutes. Investigate the validity of the airlines advertisement claim at the 5% level of significance.