Assist with assignment
Question 1[38 marks]
1.1 [11]
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. [6]
