Question 1:

For the past few years, the number of customers of a drive-in bottle shop has averaged 20 per hour. This year, another bottle shop one kilometre away opened a drive-in window. The manager of the first shop believes that this will result in a decrease in customers. A random sample of 50 hours showed an average of 18.7 customers per hour with a standard deviation of 3.0. Can we conclude at the 5% level of significance that the manager's belief is correct?

Question 2:

In recent years, fishermen have suffered financial hardship because of shortened fishing seasons, reduced catches and lower market prices. Moreover, fishermen have complained about price fluctuations and have called for a system of minimum prices. One suggestion was that the size of the catch had an immediate impact on prices and that this relationship should be clarified before potential solutions were discussed.

In an investigation of this issue, a random 12-week-period was selected to study the price of fish ($ per kg.) versus average daily catch (in 100 kgs). The data collected were analysed, and the following results were obtained:

Variable Coefficient Standard deviation p Constant 2.6344 0.3883 0.000 Catch (in 100 kgs) -0.0021755 0.0006475 0.007 R2 = 0.53