STA2601 ASSIGNMENT 4 Solutions 2026
UNISA
Unique Nr.: 135223
Opening date: 03 August 2026
Due date: 13 August 2026
,Question 1
The observed table is:
Parent Colour down White down Total
A 210 50 260
B 146 54 200
C 34 6 40
Total 390 110 500
(a) Mosaic plot and interpretation
The proportions of white chicks are:
• Parent A: 50/260 = 19.23%
• Parent B: 54/200 = 27.00%
• Parent C: 6/40 = 15.00%
A mosaic plot would therefore show that Parent B has the largest proportion of white-
coloured chicks, while Parent C has the smallest proportion.
The widths of the parent sections also represent their sample sizes: Parent A has the
largest number of chicks, followed by Parent B and then Parent C.
Interpretation: The mosaic plot suggests that the colour distribution may differ
between the three parent types, particularly because Parent B has a noticeably higher
proportion of white chicks.
(b) Hypotheses
𝐻0 : Type of parent and colour of down are independent.
𝐻1 : Type of parent and colour of down are associated.
1(c) Test statistic
Expected frequencies are calculated using:
(row total)(column total)
𝐸𝑖𝑗 =
grand total
For Parent A, coloured:
, 260(390)
𝐸= = 202.8
500
Parent A, white:
260(110)
𝐸= = 57.2
500
Similarly:
Parent Colour Expected White Expected
A 202.8 57.2
B 156.0 44.0
C 31.2 8.8
The chi-square statistic is
2
(𝑂 − 𝐸)2
𝜒 =∑
𝐸
(210 − 202.8)2 (50 − 57.2)2
𝜒2 = +
202.8 57.2
(146 − 156)2 (54 − 44)2
+ +
156 44
(34 − 31.2)2 (6 − 8.8)2
+ +
31.2 8.8
2
𝜒 = 5.218
Degrees of freedom:
𝑑𝑓 = (3 − 1)(2 − 1) = 2
At 𝛼 = 0.05:
2
𝜒0.05,2 = 5.991
Since
5.218 < 5.991
we fail to reject 𝐻0 .
UNISA
Unique Nr.: 135223
Opening date: 03 August 2026
Due date: 13 August 2026
,Question 1
The observed table is:
Parent Colour down White down Total
A 210 50 260
B 146 54 200
C 34 6 40
Total 390 110 500
(a) Mosaic plot and interpretation
The proportions of white chicks are:
• Parent A: 50/260 = 19.23%
• Parent B: 54/200 = 27.00%
• Parent C: 6/40 = 15.00%
A mosaic plot would therefore show that Parent B has the largest proportion of white-
coloured chicks, while Parent C has the smallest proportion.
The widths of the parent sections also represent their sample sizes: Parent A has the
largest number of chicks, followed by Parent B and then Parent C.
Interpretation: The mosaic plot suggests that the colour distribution may differ
between the three parent types, particularly because Parent B has a noticeably higher
proportion of white chicks.
(b) Hypotheses
𝐻0 : Type of parent and colour of down are independent.
𝐻1 : Type of parent and colour of down are associated.
1(c) Test statistic
Expected frequencies are calculated using:
(row total)(column total)
𝐸𝑖𝑗 =
grand total
For Parent A, coloured:
, 260(390)
𝐸= = 202.8
500
Parent A, white:
260(110)
𝐸= = 57.2
500
Similarly:
Parent Colour Expected White Expected
A 202.8 57.2
B 156.0 44.0
C 31.2 8.8
The chi-square statistic is
2
(𝑂 − 𝐸)2
𝜒 =∑
𝐸
(210 − 202.8)2 (50 − 57.2)2
𝜒2 = +
202.8 57.2
(146 − 156)2 (54 − 44)2
+ +
156 44
(34 − 31.2)2 (6 − 8.8)2
+ +
31.2 8.8
2
𝜒 = 5.218
Degrees of freedom:
𝑑𝑓 = (3 − 1)(2 − 1) = 2
At 𝛼 = 0.05:
2
𝜒0.05,2 = 5.991
Since
5.218 < 5.991
we fail to reject 𝐻0 .
