The Mendelian theory states that the number of a certain type of peas falling into the classifications round and yellow, wrinkled and yellow, round and green, and wrinkled and green should be in the ratio 9:3:3:1. Suppose that 100 such peas revealed 56, 19,17, and 8 in the respective categories. Are these data consistent with the model? Use 0.05 level of significance.

1.2 [16]

Mr. Acosta, a sociologist, is doing a study to see if there is a relationship between the age of a young adult (18 to 35 years old) and the type of movie preferred. A random sample of 93 young adults revealed the following data. Test whether age and type of movie preferred are independent at the 0.05 level.

Person’s Age

18-23 yr 24-29 yr 30-35 yr Row Total

Movie 18–23 yr 24–29 yr 30–35 yr Row Total

Drama

8

15

11

34

Science fiction

12

10

8

30

Comedy

9

8

12

29

Column Total

29

33

31

93

1.3 [11]

The number of accidents experienced by machinists in a certain industry were observed for a fixed period of time, with the results as shown in the companying table. Test, at the 5% level of significance, the hypothesis that data come from a Poisson.

Accident per Machinist

Frequency of Observation (number of machinists)

0

296

1

74

2

26

3

8

4

4

5

4

6

1

7

0

8

1

Question 2 [40 marks]

For the following time series

Quarter

Year

2008

2009

2010

1

26

32

34

2

50

62

70

3

40

49

50

4

33

41

15

2.1 Compute the 4-period centered moving averages. [4]

2.2 On the same axes, produce two-line graphs comparing the actual time series to the 4-period centered moving average values. Use the graph paper.

(Use 1 cm to represent 10 thousand units on the vertical axis) [4]

2.3 Compute the seasonal indexes. [10]

2.4 De-seasonalise the quarterly time series and interpret the first de-seasonalised value.

[6]

2.5 Use the method of least squares from regression analysis to determine the trend line of best fit. Use the zero-sum method for coding. [10]

2.6 Using the trend line you produced in 2.5, estimate the trend value of the time series for Quarter 3 in year 5. [3]

2.7 Find the seasonally-adjusted trend estimate value for Quarter 3 of year 5. [3]

Question 3[12 marks]

The Johnson Wholesale Company manufactures a variety of products. The prices and quanties produced for April 1994 and April 2003 are:

1994

2003

1994 Quantity

2003 Quantity

Product

Price (N$)

Price (N$)

Produced

Produced

Small motor(each)

236

288

1760

4259

Scrubbing compound( 5 litres)

296

308

86450

62949

Nails(per half kg)

40

48

9460

22370

3.1 Use 1994 as the base period to compute and interpret the price relative for 2003 for

Small motor [2]

3.2 Compute and interpret the quantity relative for Nails [2]

3.3 Construct a price index to reflect the overall change in prices of the production of the items for the period 1994 – 2003. Use the Laspeyres approach. Interpret your price index. [4]

3.3 Construct a quantity index to reflect the overall change in quantities of the production of the items for the period 1994 – 2003. Use the Paasche approach. Interpret your index. [4]

Question 4 [10 marks]

Assume the following are quarterly sales recorded for the period 2008-2011 of Food Lovers shop (in millions of NS).

Year

Quarter

Sales

2008

1

170

2

187

3

196

4

204

2009

1

153

2

195

3

162

4

144

2010

1

188

2

196

3

150

4

194

2011

1

154

2

190

3

159

4

140

4.1 Compute the exponential smoothed sales for

(i) ,

(ii) [4]

4.2 Use the Root mean squares error (RMSE) test to determine which -value produces a better forecast.

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