The Mendelian theory states that the number of a certain type of peas falling into the classifications
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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