QUESTION 1 (7 MARKS)

A manufacturer of penicillin claims that less than 12% of all people are allergic to its product. To test the claim, a random sample of 90 persons is drawn. They are treated with penicillin and 10 display an allergic reaction. Does this support the manufacturer's claim? ( = 0.05) Calculate the p-value for this test as well.

QUESTION 2 (7 MARKS)

In an investigation of the life expectancy of a certain type of mercury vapour discharge bulb, the electricity department of a municipality took a random sample of 27 bulbs for testing. It was found that s = 93.57 hours.

Does this result support the manufacturer's claim that the standard deviation is less than 100 hours? (Assume that the life expectancy is normally distributed and use = 0.05).

QUESTION 3 (36 MARKS)

The following data represents the sales (R100 000) of a beer producer for each quarter from 1990 to 1993:

	Quarterly sales	Quarterly sales	Quarterly sales	Quarterly sales
Year	I	II	III	IV
1990	24	19	25	38
1991	27	22	24	40
1992	31	23	23	41
1993	35	24	21	48

Use the data provided above to determine the following:

3.1) Represent the time series graphically. [4 marks]

3.2) Determine the least squares trend line equation for this data set, and represent it graphically. [8 marks]

3.3 ) Use the trend line equation obtained to estimate sales for the first term or 1989 and the second term of 1994 [2+2 marks]

3.4) Calculate centred four-quarterly moving averages and represent them graphically. [8 marks]

3.5) Calculate the typical seasonal index and represent these indices graphically on the same axes constructed in Question 3.4. [12 marks]

TOTAL MARKS 50 MARKS