Question 1

The data in the table below shows the usage of a basket of three food items in a household for April 2020 and May 2020.

April 2020 May 2020

Item Unit Price (N$) Quantity Unit Price (N$) Quantity

Cooking oil (750 ml) 16.00 2 16.50 3

Rice (1 kg) 25.00 3 25.40 4

Meat (1 kg) 50.00 2 50.25 2

Required:

a) Calculate and interpret the Laspeyres weighted aggregate price index for the basket of food items for May 2020. (10 Marks)

b) Calculate and interpret the Paasche weighted aggregate price index for the basket of food items for May 2020. (10 Marks)

c) Which of the food item has had the highest relative price increase between April and May 2020? Show calculations. (5 Marks)

Question 2

Standard requirements for a certain drug stipulate that the variance in drug weights must not exceed 0.03 grams (squared). A sample of five units provided the sample data as follows:

0.1 0.3 0.5 0.6 0.25

Required:

a) Use hypotheses test to determine whether the variance in the drug weights meets the standard requirements. Use =0.01 and show all the hypothesis test steps. (25 Marks)

Question 3

In 16 test runs, the fuel consumption of an experimental engine had a sample mean of 20 litres and a sample standard deviation of 2.2 litres.

Required:

a) Construct and interpret a 90% confidence interval for the population variance of the fuel consumption of the engine. (15 Marks)

Question 4

An insurance company wants to establish the relationship between the number of new policies registered by each salesperson and the number of customers contacted by each salesperson. The data in the table below was collected during the last four weeks:

Salesperson Number of customers contacted Number of new policies reqistered

1 30 10

2 25 6

3 60 15

4 20 4

5 40 15

6 55 18

7 30 10

Required:

a) Calculate/develop the least squares estimated regression equation. (15 Marks)

b) Compute and interpret the coefficient of determination. (15 Marks)

c) Calculate and interpret the correlation coefficient between the number of customers contacted and the number of new policies registered. (5 Marks)