(a) A company operates two similar factories. The CEO would like to compare the proportion of workers satisfying on their working environment. A sample of workers was taken from each factory and the results are shown as below:

Factory 1 : Sample Size: 49 Number of workers satisfying on their working environment:42

Factory 2: Sample Size: 36 Number of workers satisfying on their working environment: 33

Construct a 95% confidence interval for the difference in the true proportion of workers satisfying on their working environment between the two factories. State your assumption(s) and / or approximation(s). [8 marks]

(b) A few years ago, the owner of a fashion store decided to advertise in local television for improving sales. His records showed that without advertising, average weekly sales had been $185,000. Since he does not wish to continue spending money on advertising if sales have not increased, he decides to perform a hypothesis test. The owner determines the weekly sales for a random sample of 36 weeks in which advertising was used and obtains a mean of $198,250 and a standard deviation $23,000. What conclusion can you draw from this sample result using a 0.01 level of significance? [8 marks]