QUESTION 2 (7 MARKS) In an investigation of the life expectancy of a certain type of mercury vapor discharge bulb, the e

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QUESTION 2 (7 MARKS)
In an investigation of the life expectancy of a certain type of
mercury vapor discharge bulb, the electricity department of a
municipality took a random sample of 27 bulbs for testing. It was
found that s = 93.57 hour.
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 α = 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
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 centered 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]