Question one (5 marks)

Farmer B is planning to open a bakery in the city Oistins. One concern is the increasing cost of utilities which could make the business unprofitable; the average business is now paying $875/month. A group of consultants would like to determine the appropriate number of current businesses to survey. They want to be 97% confident in their estimate of the cost of utilities and to be within $347 of the true cost. How many businesses should the consultants survey?

Question two (8 marks)

Two machines A and B are set to produce ball bearings to fit an automotive part. Management of RPK Inc. must decide which machine to lease. They requested and got production records of the two machines. The diameter of the bearings is allowed to vary within a range of plus or minus 0.003 inches of the required diameter. Any deviation beyond 0.003 inches of the required diameter is considered substantial. Sample records indicate that when machine A was run 1000 times, 22 bearing was found to substantially deviate from the required diameter. When machine B was run 1000 times, 38 bearings were found to substantially deviate from the required diameter. Conduct a test to determine if Machine A is more than 1% better than machine B. Show your calculations and state any assumptions you make.

Question three (9 marks)

Fertilizers have been the subject of very aggressive advertising recently. To see if they serve their designed purpose, two different fertilizers (A and B) were applied to nine different types of plants. The growth rate in inches per 30 days for each type of plant is recorded below. We would like to determine if fertilizer A is better for growth than fertilizer B

A B

7 5

6 5

5 6

7 6

4 5

8 7

9 7

7 6

a. At the 5% significance level, what would you conclude? 7 marks

b. What are the limitations on your conclusion to part (a) of this question? Make your explanation in the context of this question. 2 marks

Question four (8 marks)

A developer in Oistins is in the process of deciding if to pursue purchasing a commercial real estate listing to

construct an office building. He believes the success of the venture will depend to the most recent average family income

(X) which impacts the number of office space rentals in Oistins (Y). Recently, data associating average family income (Y) ($000s) with office space rentals (X) (000s) was collected and summarized. The results are given below:

Rental Units (Y)

47

57

66

75

86

97

112

130

90

X= 1300 XY= 115461 X² = 194304

At the 0.01 level of significance, can we conclude a significant positive relationship exist between average income and the number of office space rental units in Oistins? Show your calculations. Use the p-value approach.