Question 1[38 marks]
[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]